What does the cross product of a vector mean?

And more specifically,





What is it's magnitude if vector A and B are perpendicular? Why?


What is it's magnitude if vector A and B are parallel? Why?





This isn't an example problem, it's an explanation question. 10 points to whoever is clearest and gives the most detail.|||the cross product is an operation between two vectors


it takes the magnitude of the first, say vector A, and multiplies it by the magnitude of the second, say vector B


and then, it multiplies that result (AB) by the sine of the smaller angle between the two


this





thus, the equation is: A x B = ABsin(theta)





when the vectors A and B are perpendicular, the angle between the two is pi/2


and sin(theta) is maximized at pi/2; sin(pi/2) = 1





when vectors A, B are parallel, angle between the two is 0


this is when sin(theta) is minimized, because sin(0) = 0





the cross product results in a NEW vector, with magnitude A*B and a direction that is in the direction of the third axis


say vectors A and B are on the xy plane. that means that vector A x B will be pointing in the Z-axis direction


for understanding the concept of the new direction, a picture works best


see the wikipedia link below|||A vector is like an arrow that has length and direction in space.



The cross product of two vectors is another vector which is perpendicular to both of the vectors being cross producted.



The direction of the resulting vector is dependent on which vector comes first in the cross product equation. ( "a x b" is not the same as "b x a" )



You can figure out which direction the vector goes by using this helpful picture:

http://en.wikipedia.org/wiki/File:Right_…



The magnitude of the resulting vector is equal to the magnitude of the first vector times the magnitude of the second vector times the sine of the angle between the two vectors.



Two parallel vectors cross product results in 0.



Two perpendicular vectors cross product is the magnitude of the first vector times the magnitude of the second since sine of 90 degrees is 1.