Unit Vector Notation help. What is r = a - b + c?
Q. (a) In unit vector notation, what is r = a - b + c if: a= 5i+4j-6k, b = -2i + 2j+3k, & c = 4i+3j+2k? (b) Calculate the angle between r and the positive z-axis (c) What is the component of a along the direction of b? (d) What is the component of a perpendicular to the direction of b but in the plane of a and b? I am completely lost. I have no clue how to find R, so please show your steps.
Asked by Dev - Tue Sep 8 13:25:10 2009 - - 2 Answers - 0 Comments
Q. (a) In unit vector notation, what is r = a - b + c if: a= 5i+4j-6k, b = -2i + 2j+3k, & c = 4i+3j+2k? (b) Calculate the angle between r and the positive z-axis (c) What is the component of a along the direction of b? (d) What is the component of a perpendicular to the direction of b but in the plane of a and b? I am completely lost. I have no clue how to find R, so please show your steps.
Asked by Dev - Tue Sep 8 13:25:10 2009 - - 2 Answers - 0 Comments
In Unit-Vector notation, what is the sum of the following...?
Q. In unit-vector notation, what is the sum of a = (4.0 m) i-hat + (3.0 m) j-hat and b = (-13.0 m) i-hat + (7.0 m) j-hat ? Part 2: What are the magnitude AND direction of a + b from above (in relation to i-hat)? Show and explain your work. Thanks and good luck! :)
Asked by Thick Skin - Wed Sep 12 21:54:38 2007 - - 1 Answers - 0 Comments
A. a = (4.0 , 3.0) , b = (-13.0 , 7.0) then a+b = (4.0 , 3.0) + (-13.0 , 7.0) = (4.0 - 13.0 , 3.0 + 7.0) = (-9.0 , 10.0) = -9.0i + 10.0j just add components separately part2 |a+b| = ( (-9.0)^2 + (10.0)^2 ) = 181 13.5 by pythagoras tan = 10.0 /-9.0 by gradient formula so = arctan(10.0 /-9.0) -48 = 312 the end .
Answered by The Wolf - Thu Sep 13 11:10:25 2007
Q. In unit-vector notation, what is the sum of a = (4.0 m) i-hat + (3.0 m) j-hat and b = (-13.0 m) i-hat + (7.0 m) j-hat ? Part 2: What are the magnitude AND direction of a + b from above (in relation to i-hat)? Show and explain your work. Thanks and good luck! :)
Asked by Thick Skin - Wed Sep 12 21:54:38 2007 - - 1 Answers - 0 Comments
A. a = (4.0 , 3.0) , b = (-13.0 , 7.0) then a+b = (4.0 , 3.0) + (-13.0 , 7.0) = (4.0 - 13.0 , 3.0 + 7.0) = (-9.0 , 10.0) = -9.0i + 10.0j just add components separately part2 |a+b| = ( (-9.0)^2 + (10.0)^2 ) = 181 13.5 by pythagoras tan = 10.0 /-9.0 by gradient formula so = arctan(10.0 /-9.0) -48 = 312 the end .
Answered by The Wolf - Thu Sep 13 11:10:25 2007
What is the polar notation for a vector that points from the origin to the point (0, 3.00)?
Q. Basically, what is and how do I write polar notation?
Asked by kujo - Wed Apr 1 17:37:17 2009 - - 1 Answers - 0 Comments
A. On the normal convention, the x-axis is = 0 and increases as you go to the y-axis. On this convention, a point [r, ] in polar coordinates becomes the point (r cos , r sin ) in xy-coordinates. If you want (0, 3), then you need: r cos = 0 r sin = 3 The first equation can be handled in two ways: either r is zero or cos is zero. But it can't be the first, because that would make the second equation into 0 = 3. So it must be that cos = 0. Where cosine is 0, the sine is either +1 or -1. Since the radius r should always be positive, we choose that sin = +1, which happens at = /2 + 2 N, for all integer N. (This always happens with polar coordinates -- you usually ignore the N > 1 and N < -1, but sometimes you've got… [cont.]
Answered by Drostie - Wed Apr 1 18:01:11 2009
Q. Basically, what is and how do I write polar notation?
Asked by kujo - Wed Apr 1 17:37:17 2009 - - 1 Answers - 0 Comments
A. On the normal convention, the x-axis is = 0 and increases as you go to the y-axis. On this convention, a point [r, ] in polar coordinates becomes the point (r cos , r sin ) in xy-coordinates. If you want (0, 3), then you need: r cos = 0 r sin = 3 The first equation can be handled in two ways: either r is zero or cos is zero. But it can't be the first, because that would make the second equation into 0 = 3. So it must be that cos = 0. Where cosine is 0, the sine is either +1 or -1. Since the radius r should always be positive, we choose that sin = +1, which happens at = /2 + 2 N, for all integer N. (This always happens with polar coordinates -- you usually ignore the N > 1 and N < -1, but sometimes you've got… [cont.]
Answered by Drostie - Wed Apr 1 18:01:11 2009
Unit Vector Notation question?
Q. Vector A has the magnitude 12.9 m and is angled 57.6 counterclockwise from the positive direction of the x axis of an xy coordinate system. Also, Vector B = (13.2 m)i + (5.21 m)j on that same coordinate system. We now rotate the system counterclockwise about the origin by 16.9 to form an x'y' system. On this new system, what are (a) Vector A and (b) Vector B, both in unit-vector notation?
Asked by Arslan K - Mon Jun 8 18:11:57 2009 - - 1 Answers - 0 Comments
A. /// x=x'costheta-y'sintheta y=x'sintheta+y'costheta the new value would b x,y x'=13.2 y'=5.21 theta=16.9 plug and chuck
Answered by vect - Mon Jun 8 21:00:33 2009
Q. Vector A has the magnitude 12.9 m and is angled 57.6 counterclockwise from the positive direction of the x axis of an xy coordinate system. Also, Vector B = (13.2 m)i + (5.21 m)j on that same coordinate system. We now rotate the system counterclockwise about the origin by 16.9 to form an x'y' system. On this new system, what are (a) Vector A and (b) Vector B, both in unit-vector notation?
Asked by Arslan K - Mon Jun 8 18:11:57 2009 - - 1 Answers - 0 Comments
A. /// x=x'costheta-y'sintheta y=x'sintheta+y'costheta the new value would b x,y x'=13.2 y'=5.21 theta=16.9 plug and chuck
Answered by vect - Mon Jun 8 21:00:33 2009
If using vector notation, what does this mean: a b?
Q. If using vector notation, what does this mean: a b?
Asked by Michael M - Tue Jan 15 15:49:48 2008 - - 2 Answers - 0 Comments
A. Yes, you could look it up but that somewhat undermines the purpose of Yahoo Answers! It is the vector product or cross product of the two vectors a and b (which should be in bold to denote that they are vectors). It is a vector quantity. It is defined as being equal to the product of 4 things: the magnitude of a, the magnitude of b, the sine of the angle between them and the unit normal vector, n, in the direction perpendicular to both (using a right handed corkscrew convention). So, if a is along the x-axis and b along the y-axis then n would be up the z-axis. It should be clear that i^j=k Magnitude just means size or length. A unit vector has a length of 1. The vector product is NOT commutative. In fact, it is anti-commutative.… [cont.]
Answered by Perspykashus - Wed Jan 16 07:06:13 2008
Q. If using vector notation, what does this mean: a b?
Asked by Michael M - Tue Jan 15 15:49:48 2008 - - 2 Answers - 0 Comments
A. Yes, you could look it up but that somewhat undermines the purpose of Yahoo Answers! It is the vector product or cross product of the two vectors a and b (which should be in bold to denote that they are vectors). It is a vector quantity. It is defined as being equal to the product of 4 things: the magnitude of a, the magnitude of b, the sine of the angle between them and the unit normal vector, n, in the direction perpendicular to both (using a right handed corkscrew convention). So, if a is along the x-axis and b along the y-axis then n would be up the z-axis. It should be clear that i^j=k Magnitude just means size or length. A unit vector has a length of 1. The vector product is NOT commutative. In fact, it is anti-commutative.… [cont.]
Answered by Perspykashus - Wed Jan 16 07:06:13 2008
Can kinetic energy be expressed in unit-vector notation?
Q. In my homework problem we have to find velocity in unit vector notation, and then use that to find the kinetic energy using the formula 1/2 m v squared. I thought that when I squared a vector I had to use the dot product formul (ai + bj)(ai + bj) = a squared + b squared, giving you a single number without any "i"s or "j"s. Earlier in the question it says that we should use unit-vector notation for all the answers. How can I do that for the kinetic energy portion? Thanks!
Asked by Heather - Sun Mar 29 16:17:53 2009 - - 1 Answers - 0 Comments
A. No, kinetic energy is a scalar, not a vector. The v that appears in the formula for KE is really the speed, the magnitude of the velocity vector. However, v^2 is the same as the dot product of the velocity vector with itself, so you could write the formula in terms of the velocity vector as KE = (1/2) * m (v . v) where "." means dot product and "v" means velocity vector. The result is not a vector.
Answered by Randy P - Sun Mar 29 16:36:57 2009
Q. In my homework problem we have to find velocity in unit vector notation, and then use that to find the kinetic energy using the formula 1/2 m v squared. I thought that when I squared a vector I had to use the dot product formul (ai + bj)(ai + bj) = a squared + b squared, giving you a single number without any "i"s or "j"s. Earlier in the question it says that we should use unit-vector notation for all the answers. How can I do that for the kinetic energy portion? Thanks!
Asked by Heather - Sun Mar 29 16:17:53 2009 - - 1 Answers - 0 Comments
A. No, kinetic energy is a scalar, not a vector. The v that appears in the formula for KE is really the speed, the magnitude of the velocity vector. However, v^2 is the same as the dot product of the velocity vector with itself, so you could write the formula in terms of the velocity vector as KE = (1/2) * m (v . v) where "." means dot product and "v" means velocity vector. The result is not a vector.
Answered by Randy P - Sun Mar 29 16:36:57 2009
Projectile help...projectile in vector notation?
Q. A projectile is launched from the ground with velocity v = (7i + 24j) m/s. (a)What is the magnitude of its velocity at maximum height? (b)What is the velocity (in vector notation) just before it strikes the ground? (c)What is the magnitude of the change in momentum of the projectile between leaving the ground and landing again? Take the mass of the projectile to be 2 kg. AIP, how did u get polar form of 25 m/s or in degrees?? I thought that at maximum height, magnitude would be zero? Do explain..
Asked by Ann B - Fri Oct 10 13:55:25 2008 - - 1 Answers - 0 Comments
A. vi = (7i + 24j) = In polar form = 25 m/s @ 73.74 degrees vx = 7 m/s --->(a) vy = 24 m/s vxf = 7 m/s vyf = -24 j m/s vf = <7 i - 24 j> m/s --->(b) P = m*(vf - vi) P = 2*(7 i - 24 j - 7i - 24j P = 2*(0i - 48j) P = -96 j kg m/s What is the magnitude... 96 kg m/s --->(c) Edit: Initial Polar form: V = sqr(7^2+24^2) = 25 angle = Arctan (24/7) =73.739 degrees Vx = 7 m/s is constant even at maximum height, but Vy---> zero at max-height
Answered by unknown - Fri Oct 10 17:25:29 2008
Q. A projectile is launched from the ground with velocity v = (7i + 24j) m/s. (a)What is the magnitude of its velocity at maximum height? (b)What is the velocity (in vector notation) just before it strikes the ground? (c)What is the magnitude of the change in momentum of the projectile between leaving the ground and landing again? Take the mass of the projectile to be 2 kg. AIP, how did u get polar form of 25 m/s or in degrees?? I thought that at maximum height, magnitude would be zero? Do explain..
Asked by Ann B - Fri Oct 10 13:55:25 2008 - - 1 Answers - 0 Comments
A. vi = (7i + 24j) = In polar form = 25 m/s @ 73.74 degrees vx = 7 m/s --->(a) vy = 24 m/s vxf = 7 m/s vyf = -24 j m/s vf = <7 i - 24 j> m/s --->(b) P = m*(vf - vi) P = 2*(7 i - 24 j - 7i - 24j P = 2*(0i - 48j) P = -96 j kg m/s What is the magnitude... 96 kg m/s --->(c) Edit: Initial Polar form: V = sqr(7^2+24^2) = 25 angle = Arctan (24/7) =73.739 degrees Vx = 7 m/s is constant even at maximum height, but Vy---> zero at max-height
Answered by unknown - Fri Oct 10 17:25:29 2008
How do you do this vector question?
Q. (a) What is the sum of the following four vectors in unit-vector notation? For that sum, what are (b) the magnitude, (c) the angle in degrees, and (d) the angle in radians? E: 6.00m at +9.00 rad , F: 5.00m at -75.0degrees G: 4.00m at +1.20 rad , H: 6.00m at -210degrees
Asked by bryon_barker - Tue Jan 22 21:53:25 2008 - - 1 Answers - 0 Comments
A. You may solve this kind of problems graphically with a geometric method. But it would be very troublesome for me to plot and show to you. Besides, I do not know your geometry background. Hence here I will show you an analytical way. First convert every thing to x-y coordinates (unit in meter): E: (6.00*cos 9.00, 6.00*sin 9.00) F: (5.00*cos 75.0 , -5.00*sin 75.0 ) G: (4.00*cos 1.20, 4.00*sin 1.20) H: (6.00*cos 210 , -6.00*sin 210 ) Second perform the summation: S = (6.00*cos 9.00 + 5.00*cos 75.0 + 4.00*cos 1.20 + 6.00*cos 210 , 6.00*sin 9.00 - 5.00*sin 75.0 + 4.00*sin 1.20 - 6.00*sin 210 ) = (6.00*cos 9.00 + 5.00*cos 75.0 + 4.00*cos 1.20 + 6.00*cos 210 )i + (6.00*sin 9.00 - 5.00*sin 75.0 + 4.00*sin 1.20 - 6.00*sin 210 )j = I*i + J*j [cont.]
Answered by Hahaha - Thu Jan 24 18:15:18 2008
Q. (a) What is the sum of the following four vectors in unit-vector notation? For that sum, what are (b) the magnitude, (c) the angle in degrees, and (d) the angle in radians? E: 6.00m at +9.00 rad , F: 5.00m at -75.0degrees G: 4.00m at +1.20 rad , H: 6.00m at -210degrees
Asked by bryon_barker - Tue Jan 22 21:53:25 2008 - - 1 Answers - 0 Comments
A. You may solve this kind of problems graphically with a geometric method. But it would be very troublesome for me to plot and show to you. Besides, I do not know your geometry background. Hence here I will show you an analytical way. First convert every thing to x-y coordinates (unit in meter): E: (6.00*cos 9.00, 6.00*sin 9.00) F: (5.00*cos 75.0 , -5.00*sin 75.0 ) G: (4.00*cos 1.20, 4.00*sin 1.20) H: (6.00*cos 210 , -6.00*sin 210 ) Second perform the summation: S = (6.00*cos 9.00 + 5.00*cos 75.0 + 4.00*cos 1.20 + 6.00*cos 210 , 6.00*sin 9.00 - 5.00*sin 75.0 + 4.00*sin 1.20 - 6.00*sin 210 ) = (6.00*cos 9.00 + 5.00*cos 75.0 + 4.00*cos 1.20 + 6.00*cos 210 )i + (6.00*sin 9.00 - 5.00*sin 75.0 + 4.00*sin 1.20 - 6.00*sin 210 )j = I*i + J*j [cont.]
Answered by Hahaha - Thu Jan 24 18:15:18 2008
Angular momentum using vector notations?
Q. The position vector of a particle of mass 4 kg is given by vector r = 7 i + 3t^2 j , where r is in meters and t is in seconds. Determine the angular momentum and torque acting on the particle about the origin.
Asked by darken4life - Wed Oct 22 18:19:47 2008 - - 1 Answers - 0 Comments
A. angular momentum = L = r x p = r x mv, where v = dr/dt = 6t j L = r x p = (7 i + 3t^2 j) x 4(6t j) L = (7 i + 3t^2 j) x 24t j L = (7*24t) k L = 168t N-m-s (k) Torque = T = r x F = dL/dt L = 168t T = 168 N-m (k)
Answered by mecdub - Wed Oct 22 19:18:15 2008
Q. The position vector of a particle of mass 4 kg is given by vector r = 7 i + 3t^2 j , where r is in meters and t is in seconds. Determine the angular momentum and torque acting on the particle about the origin.
Asked by darken4life - Wed Oct 22 18:19:47 2008 - - 1 Answers - 0 Comments
A. angular momentum = L = r x p = r x mv, where v = dr/dt = 6t j L = r x p = (7 i + 3t^2 j) x 4(6t j) L = (7 i + 3t^2 j) x 24t j L = (7*24t) k L = 168t N-m-s (k) Torque = T = r x F = dL/dt L = 168t T = 168 N-m (k)
Answered by mecdub - Wed Oct 22 19:18:15 2008
What is the momentum vector of the second ball?
Q. A 500 g ball traveling in the +x direction at 4.0 m/s collides with and bounces off another ball of mass 1.5 kg which is initially not moving. After the collision the momentum vector of the first ball is (2, 2.5) kg-m/s, where the notation is of components in the (x, y) directions. What is the momentum vector of the second ball, again in units of kg-m/s?
Asked by katie w - Sun Mar 8 21:02:31 2009 - - 2 Answers - 0 Comments
A. The way the problem is stated, there actually is no solution, because the energy within the system increased for no apparent reason. Before the collison, the 500 g ball had a velocity of magnitude 4.0 m/s, and the 1.5 kg ball had a velocity of magnitude zero. After the collision, the 500g ball has a velocity of magnitude square_root(41) m/s. Since the 1.5 kg ball was at rest initially, there is no source for the increased kinetic energy. I think that this was intended as a conservation of momentum problem and that your textbook author was just sloppy. Treated as a conservation of momentum problem the solution is simple. The sum of the initial momentums is equal to the sum of the final momentums. Momentum is, of course, p = mv. (I… [cont.]
Answered by ecmfw - Wed Mar 11 13:18:18 2009
Q. A 500 g ball traveling in the +x direction at 4.0 m/s collides with and bounces off another ball of mass 1.5 kg which is initially not moving. After the collision the momentum vector of the first ball is (2, 2.5) kg-m/s, where the notation is of components in the (x, y) directions. What is the momentum vector of the second ball, again in units of kg-m/s?
Asked by katie w - Sun Mar 8 21:02:31 2009 - - 2 Answers - 0 Comments
A. The way the problem is stated, there actually is no solution, because the energy within the system increased for no apparent reason. Before the collison, the 500 g ball had a velocity of magnitude 4.0 m/s, and the 1.5 kg ball had a velocity of magnitude zero. After the collision, the 500g ball has a velocity of magnitude square_root(41) m/s. Since the 1.5 kg ball was at rest initially, there is no source for the increased kinetic energy. I think that this was intended as a conservation of momentum problem and that your textbook author was just sloppy. Treated as a conservation of momentum problem the solution is simple. The sum of the initial momentums is equal to the sum of the final momentums. Momentum is, of course, p = mv. (I… [cont.]
Answered by ecmfw - Wed Mar 11 13:18:18 2009
GCSE Mathematical Vector problems?
Q. Hey. I've recently started the topic of Vectors in my mathematics book. I've gone throught vector notation, vector addition, vector subtraction and scalar multiplication. I've gone onto 'Using Vectors' which is basically geometric vectors such as describing position and typical geometrical problems. I'm having major problems with these. Can someone please help? All comments are very much appreciated.
Asked by Jay Garrick - Sat Sep 20 16:18:16 2008 - - 1 Answers - 0 Comments
A. en.wikipedia.org/wiki/Vec tor_(spatial)
Answered by Straightedge - Sun Sep 21 02:29:14 2008
Q. Hey. I've recently started the topic of Vectors in my mathematics book. I've gone throught vector notation, vector addition, vector subtraction and scalar multiplication. I've gone onto 'Using Vectors' which is basically geometric vectors such as describing position and typical geometrical problems. I'm having major problems with these. Can someone please help? All comments are very much appreciated.
Asked by Jay Garrick - Sat Sep 20 16:18:16 2008 - - 1 Answers - 0 Comments
A. en.wikipedia.org/wiki/Vec tor_(spatial)
Answered by Straightedge - Sun Sep 21 02:29:14 2008
Geometrical Vector problems?
Q. Hey. I've recently started the topic of Vectors in my mathematics book. I've gone throught vector notation, vector addition, vector subtraction and scalar multiplication. I've gone onto 'Using Vectors' which is basically geometric vectors such as describing position and typical geometrical problems. I'm having major problems with these. Can someone please help? All comments are very much appreciated. Many thanks!
Asked by Jay Garrick - Sat Sep 20 15:33:24 2008 - - 1 Answers - 0 Comments
A. en.wikipedia.org/wiki/Vec tor_(spatial)
Answered by Straightedge - Sun Sep 21 02:29:43 2008
Q. Hey. I've recently started the topic of Vectors in my mathematics book. I've gone throught vector notation, vector addition, vector subtraction and scalar multiplication. I've gone onto 'Using Vectors' which is basically geometric vectors such as describing position and typical geometrical problems. I'm having major problems with these. Can someone please help? All comments are very much appreciated. Many thanks!
Asked by Jay Garrick - Sat Sep 20 15:33:24 2008 - - 1 Answers - 0 Comments
A. en.wikipedia.org/wiki/Vec tor_(spatial)
Answered by Straightedge - Sun Sep 21 02:29:43 2008
Three forces on an object, looking for the acceleration in unit-vector, and as a magnitude. And Direction?
Q. Three forces, are pushing on an object in space, an asteroid, weighing in at 120 kg. Here is a free-body-diagram of the forces on a y x axis. What is the asteroids acceleration (a) in unit-vector notation, and as (b) a magnitude. (c) What is the direction of the asteroid? Explain please
Asked by Thick Skin - Sat Sep 30 23:09:06 2006 - - 2 Answers - 1 Comments
A. The three forces are a 32 newton force directed along a vector making a + 30 deg angle with the positive x-axis, a 41 newton force directed -60 degrees with respect to the +x axis, and a 55 newton force directed along the +x axis. The total force on the object is the vector sum of these forces, and the object's vector acceleration is given by the force vector divided by the object's mass (from F = m*a). THe problem describes the force vectors in terms of their polar coordinates (r, theta), where r is the vector magnitude and theta is the angle with respect to the +x axis. To add the force vectors, you need to resolve the vectors into their x and y components in rectangular (Cartesian) coordinates. In general, for a vector given in… [cont.]
Answered by hfshaw - Sun Oct 1 02:43:53 2006
Q. Three forces, are pushing on an object in space, an asteroid, weighing in at 120 kg. Here is a free-body-diagram of the forces on a y x axis. What is the asteroids acceleration (a) in unit-vector notation, and as (b) a magnitude. (c) What is the direction of the asteroid? Explain please
Asked by Thick Skin - Sat Sep 30 23:09:06 2006 - - 2 Answers - 1 Comments
A. The three forces are a 32 newton force directed along a vector making a + 30 deg angle with the positive x-axis, a 41 newton force directed -60 degrees with respect to the +x axis, and a 55 newton force directed along the +x axis. The total force on the object is the vector sum of these forces, and the object's vector acceleration is given by the force vector divided by the object's mass (from F = m*a). THe problem describes the force vectors in terms of their polar coordinates (r, theta), where r is the vector magnitude and theta is the angle with respect to the +x axis. To add the force vectors, you need to resolve the vectors into their x and y components in rectangular (Cartesian) coordinates. In general, for a vector given in… [cont.]
Answered by hfshaw - Sun Oct 1 02:43:53 2006
How do i write a sum of the pairs of vectors in an ordered pair notation?
Q. one arrow hits (-4,-4) the other hits (8,-4)
Asked by girlfrommarina16 - Fri May 1 03:03:49 2009 - - 1 Answers - 0 Comments
Q. one arrow hits (-4,-4) the other hits (8,-4)
Asked by girlfrommarina16 - Fri May 1 03:03:49 2009 - - 1 Answers - 0 Comments
What is the direction of the vector C = (A - B) measured as an angle between the vector C....?
Q. The x-and y-components of two vectors A and B in the notation (x, y) are (3.209, 3.832) for A and (-6.848, -4.313) for B in arbitrary units. What is the direction of the vector C = (A - B) measured as an angle between the vector C and the positive x-axis in counter clockwise direction
Asked by Princess - Sun Feb 10 20:24:24 2008 - - 1 Answers - 0 Comments
Q. The x-and y-components of two vectors A and B in the notation (x, y) are (3.209, 3.832) for A and (-6.848, -4.313) for B in arbitrary units. What is the direction of the vector C = (A - B) measured as an angle between the vector C and the positive x-axis in counter clockwise direction
Asked by Princess - Sun Feb 10 20:24:24 2008 - - 1 Answers - 0 Comments
Vectors Notation?
Q. Hey, what is the difference between AB and AB with an arrow over it. I'm guessing one is a vector the other is a scalar? Why does |AB[arrow]| = |AB| Thanks
Asked by Philip J - Sun Jan 21 05:59:41 2007 - - 6 Answers - 0 Comments
A. Yes Philip, you're right. AB without the arrow refers to the scalar, which then means the magnitude. Whereas AB with the arrow on top refers to the vector and thus the direction needs to be included. eg. AB(->) = 3i+4j, AB = square root of (3 +4 )=5 hmm... lAB(->)l=lABl cause they refer to the same thing. Just as I mentioned above, AB with the arrow refers to the vector and the absolute bars refers to the magnitude of the vector, hence they are equivalent mathematical terms.
Answered by tabletennisrulez - Sun Jan 21 06:13:13 2007
Q. Hey, what is the difference between AB and AB with an arrow over it. I'm guessing one is a vector the other is a scalar? Why does |AB[arrow]| = |AB| Thanks
Asked by Philip J - Sun Jan 21 05:59:41 2007 - - 6 Answers - 0 Comments
A. Yes Philip, you're right. AB without the arrow refers to the scalar, which then means the magnitude. Whereas AB with the arrow on top refers to the vector and thus the direction needs to be included. eg. AB(->) = 3i+4j, AB = square root of (3 +4 )=5 hmm... lAB(->)l=lABl cause they refer to the same thing. Just as I mentioned above, AB with the arrow refers to the vector and the absolute bars refers to the magnitude of the vector, hence they are equivalent mathematical terms.
Answered by tabletennisrulez - Sun Jan 21 06:13:13 2007
What is the dimension of the vector space of all 3x3 skew symmetric matrices?
Q. Find a basis... Please show details and use general notation of matrix.
Asked by Hassan Farouk - Fri Jan 16 06:28:54 2009 - - 1 Answers - 0 Comments
A. I'm going to say 3: with [0 1 0, -1 0 0, 0 0 0] [0 0 1, 0 0 0, -1 0 0] [0 0 0, 0 0 1, 0 -1 0] I think you could construct them all.
Answered by supastremph - Fri Jan 16 07:42:33 2009
Q. Find a basis... Please show details and use general notation of matrix.
Asked by Hassan Farouk - Fri Jan 16 06:28:54 2009 - - 1 Answers - 0 Comments
A. I'm going to say 3: with [0 1 0, -1 0 0, 0 0 0] [0 0 1, 0 0 0, -1 0 0] [0 0 0, 0 0 1, 0 -1 0] I think you could construct them all.
Answered by supastremph - Fri Jan 16 07:42:33 2009
Physics Vector Question?
Q. OK, I'm studying beginner's physics, but this x'y' mapping system is beyond me. Here's the question in the book, if someone can explain the mapping system in simple English (the book's explanation is over my head!) and/or show me how to solve this equation, I'd be very grateful! (Thankful AND 10 points worth of grateful!) Two coordinate systems are used to describe four vectors. The xy-axes point horizontal and vertical and the x'y'-axes are rotated from the xy-axes by an angle . In unit vector notation the four vectors are, A = A i B = B j C = C i' D = D j'. The four vectors satisfy the vector equation, A + D = B + C. As, well the magnitudes of C and D satisfy the relation C = kD. Given that = 44 , k = 0.39 and B = 37,… [cont.]
Asked by Sara P - Tue Sep 16 23:13:48 2008 - - 1 Answers - 0 Comments
A. you are recycling characters that is why it is hard to see it here . (you used A = Ai ... which makes it not easy to see it at first.) A = ai B = bj (b = 37) C = ci' (c = 0.39d) D = dj' now, with rotation: i' = cos i + sin j j' = cos +90 i + sin +90 j = -sin i + cos j C = 0.719c i + 0.695c j D = -0.695d i + 0.719d j ai + -0.695d i + 0.719d j = 37 j + 0.719c i + 0.695c j now, c = 0.39d (a - 0.695d)i + 0.719d j = 0.28041d i + (37 + 0.27105d) j two vectors are equal if their corresponding components are equal. observing the j components first: 0.719d = 37 + 0.27105d d = 82.5985 also a - 0.695d = 0.28041d a = 0.97541d a = 80.5674 thus A = 80.5674 i
Answered by Alam Ko Iyan - Tue Sep 16 23:45:27 2008
Q. OK, I'm studying beginner's physics, but this x'y' mapping system is beyond me. Here's the question in the book, if someone can explain the mapping system in simple English (the book's explanation is over my head!) and/or show me how to solve this equation, I'd be very grateful! (Thankful AND 10 points worth of grateful!) Two coordinate systems are used to describe four vectors. The xy-axes point horizontal and vertical and the x'y'-axes are rotated from the xy-axes by an angle . In unit vector notation the four vectors are, A = A i B = B j C = C i' D = D j'. The four vectors satisfy the vector equation, A + D = B + C. As, well the magnitudes of C and D satisfy the relation C = kD. Given that = 44 , k = 0.39 and B = 37,… [cont.]
Asked by Sara P - Tue Sep 16 23:13:48 2008 - - 1 Answers - 0 Comments
A. you are recycling characters that is why it is hard to see it here . (you used A = Ai ... which makes it not easy to see it at first.) A = ai B = bj (b = 37) C = ci' (c = 0.39d) D = dj' now, with rotation: i' = cos i + sin j j' = cos +90 i + sin +90 j = -sin i + cos j C = 0.719c i + 0.695c j D = -0.695d i + 0.719d j ai + -0.695d i + 0.719d j = 37 j + 0.719c i + 0.695c j now, c = 0.39d (a - 0.695d)i + 0.719d j = 0.28041d i + (37 + 0.27105d) j two vectors are equal if their corresponding components are equal. observing the j components first: 0.719d = 37 + 0.27105d d = 82.5985 also a - 0.695d = 0.28041d a = 0.97541d a = 80.5674 thus A = 80.5674 i
Answered by Alam Ko Iyan - Tue Sep 16 23:45:27 2008
Unit-vector?
Q. In a unit-vector notation, what is the sun of a = (4.00 m) i^ + (3.0 M)j^ and b = (-13.0 m)i^ + (7.0 m)j^ ? (the ^ next the the letters are hats, so i^ would be i hat) What are the (b) magnitude and (c) direction of a + c (relative to i^)?
Asked by Thick Skin - Sun Sep 17 23:46:35 2006 - - 1 Answers - 0 Comments
A. simple addition my friend... a+b=(4.00-13.0m)i+(7.0+3. 0m)j c=(-9.00m)i+(10.0m)j ...magnitude is just the sum of the components so... |c|=sqr[(-9.00m)^2+(10.0m )^2] the direction in radians with respect to i roof is: tan =(j/i) =tan^-1(10.0m/-9.00m)
Answered by venomfx - Mon Sep 18 00:09:58 2006
Q. In a unit-vector notation, what is the sun of a = (4.00 m) i^ + (3.0 M)j^ and b = (-13.0 m)i^ + (7.0 m)j^ ? (the ^ next the the letters are hats, so i^ would be i hat) What are the (b) magnitude and (c) direction of a + c (relative to i^)?
Asked by Thick Skin - Sun Sep 17 23:46:35 2006 - - 1 Answers - 0 Comments
A. simple addition my friend... a+b=(4.00-13.0m)i+(7.0+3. 0m)j c=(-9.00m)i+(10.0m)j ...magnitude is just the sum of the components so... |c|=sqr[(-9.00m)^2+(10.0m )^2] the direction in radians with respect to i roof is: tan =(j/i) =tan^-1(10.0m/-9.00m)
Answered by venomfx - Mon Sep 18 00:09:58 2006
Is the moment of a body a vector quantity?
Q. I'm thinking it is because it does have a dirction either clockwise or anticlockwise. Can anyone explain to me why it is or isn't and hence could it be solved in i and j notation?
Asked by oli - Thu Jun 4 11:40:29 2009 - - 3 Answers - 0 Comments
A. it is a vector and your right of thinking of clockwise and anticlockwise directions. A moment is the same as torque and torque is defined as the cross product of the force vector and the lever arm vector, and as you probably know the result of any cross product produces a third vector that is perpendicular two both other vectors. The moment or torque of a body can be represented in unit vector notation (i j k) by using the determent method in this case M= FXr = det |i j k | |Fi Fj Fk| |ri rj rk| sorry about the above if you don't know this or cannot understand the above wikipedia cross product
Answered by jason f - Thu Jun 4 12:05:53 2009
Q. I'm thinking it is because it does have a dirction either clockwise or anticlockwise. Can anyone explain to me why it is or isn't and hence could it be solved in i and j notation?
Asked by oli - Thu Jun 4 11:40:29 2009 - - 3 Answers - 0 Comments
A. it is a vector and your right of thinking of clockwise and anticlockwise directions. A moment is the same as torque and torque is defined as the cross product of the force vector and the lever arm vector, and as you probably know the result of any cross product produces a third vector that is perpendicular two both other vectors. The moment or torque of a body can be represented in unit vector notation (i j k) by using the determent method in this case M= FXr = det |i j k | |Fi Fj Fk| |ri rj rk| sorry about the above if you don't know this or cannot understand the above wikipedia cross product
Answered by jason f - Thu Jun 4 12:05:53 2009
From Yahoo Answer Search: 'Vector notation'
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Wed, 29 Jul 2009 14:29:00 GM
And x can be a function (or . vector. ) in a Hilbert Space too (a constant function if you wish). Then if f:H -> H rather than f: R->R then the . notation. wouldn't be a problem. I think math is weird/interesting because the further you go in ...
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