# Cross product

## Homework Statement

a) Let v be a unit vector in R^3 and u be a vector which is orthogonal to v. Show v x (v x u) = -u
b) Let v and u be orthogonal unit vectors in R^3. Show u x (v x (v x (v x u))) = -v

## The Attempt at a Solution

I am very lost in this question, I know a unit vector is = 1 therefore the summuation of the vector v is 1 for example, v = (1,0,0). square root(1^2 + 0 + 0) = 1 and i know u dot v is 0 but how do i start the prove?

thank you

Defennder
Homework Helper
Apply the http://en.wikipedia.org/wiki/Triple_product" [Broken] for the first one then simplify. Do it repeatedly for the second.

Last edited by a moderator:
matt grime
$$\vec{u}\times\vec{v}= \left|\begin{array}{ccc}\vec{i} & \vec{j} & \vec{k} \\ a & 0 & 0 \\0 & b & 0\end{array}\right|$$