u•w = v•w
u•w - v•w = 0
(u-v)•w = 0
so u-v is orthogonal to w
u×w = v×w
u×w - v×w = 0
(u-v)×w = 0
so u-v is parallel to w
so, u-v = 0
u=v
I will be using != for not equal
The cancellation law for real numbers is quite obvious: if a,b, and c != 0 are real numbers for which ac = bc then a = b. It is natural to ask if the cancellation law holds for three dimensional vectors.
If U x W = V x W, U (dot) W = V (dot) W, and W != 0, is it true that U = V? If Yes Prove it. If no give a counter example.
1 answer
1 answer