- #1
geoffrey159
- 535
- 72
Homework Statement
If ##u,v,w\in\mathbb{R}^3##, show that ## u\times(v\times w) = (u.w) v - (u.v) w ##.
Homework Equations
The Attempt at a Solution
Since ## u\times(v\times w)##, ##v## and ##w## are orthogonal to ##v\times w##, these vectors are coplanar. Therefore, there must be reals ## a,b## such that ## u\times(v\times w) = a v + b w ##.
Then, ## 0 = u.(u\times(v\times w)) = a u.v + b u.w ## and ## a = u.w## and ## b = - u.v## work. But why not ## a = -u.w ## and ## b = u.v ## ? Thanks