Prove (u+v) x (u-v) = 2v x u (Cross product)

[ohiggins]

Homework Statement

Show that (u+v) x (u-v) = 2v x u

Homework Equations

being u=(x₁,y₁,z₁)
and v= u=(x₂,y₂,z₂)

The Attempt at a Solution

I've got 2v x u equals:

(2y₂.z₁ - 2z₂.y₁) + (2x₂.z₁ - 2z₂.x₁) +
(2x₂.y₁ - 2y₂.x₁)

But I'm nearly to melt my mind to prove (u+v) x (u-v) = above

 

[ehild]

Expand the product, and use that property of the cross product that uxv=-vxu and the product of identical vectors is zero.

ehild