Question

PLEASE HELP! - LINEAR ALGEBRA

Suppose u, v and w are 3-dimensional vectors.

a) Show that u x (v x w) = (u dot w)v - (u dot v)w

b) Deduce that (u x v) x w = (u dot w)v - (v dot w)u

KEY: x = cross product and dot = dot product

* For 9b, you must use 9a to deduce it.

Answer 1

I would suggets letting u = [u1, u2, u3], v = [v1, v2, v3] and w = [w1, w2, w3] and just perform the operations on the right side, then do the ones on the left side and they should be equal.. although this is kind of a long calculation i could do it andsee what gives

Answer 2

That is a good idea. I will try that in the morning. For now I have to get sleep! Haha. If you decide to work on it, please let me know how it goes. I will contact you once I attempt it myself. Thanks! @kirbykirby

Answer 3

Ok I can try after but I also have some work to do now lol. It's just a very long calculation, but it should be fairly straightforward though. As long as you respect the order of importance (do what's in the parentheses first) and apply the definition of cross products and dot products, it should somehow work