Question

If u is nonzero and u, v and w are vectors, is it valid to cancel u from both sides of the equation u x v = u x w and conclude that v=w? Explain your reasoning.

Answer 1

no it isnt
in this case
u can say

u x v = u x w

hence
u x v - u x w = 0
u x (v-w) = 0

so we see that u is collinear to (v-w) hence

u = t(v-w) where t is any real parameter

Answer 2

get it?

Answer 3

What's collinear?

Answer 4

means the two vectors run parallel to each other

Answer 5

oh okay make sense thanks

Answer 6

actually one more question how do you know that u x (v-w) is parallel? it's cross product

Answer 7

when the cross product of 2 vectors is 0 that mean theyre parallel to each other

see
a x b = absint
where t is the angle b/w the vectors

a x b = 0 and vectors are both nonzero
so => sin t = 0

the angle bw the vectors is zero

Answer 8

oh yeah okay thanks a lot man