# Lagrange Triple Vector proof

1. Sep 9, 2008

### l46kok

1. The problem statement, all variables and given/known data
Prove

$$a \times (b \times c) = (a * c)b - (a*b)c$$

For orthagonal coordinates, a,b,c

2. Relevant equations

Cross Product and Dot Product

3. The attempt at a solution

I thought about expanding both sides out and proving they are equal, but I just realized that the left side of the theorem would give me a vector and the right side would give me a scalar. Perhaps I don't understand the theorem perfectly. Can someone explain the notion about this theorem and how I would go about proving it?

2. Sep 9, 2008

### l46kok

I should clarify a bit

a,b,c are for cartesian orthagonal coordinates (i,j,k vectors are all normal to each other)

3. Sep 9, 2008

### Dick

If a,b and c are vectors the right side IS a vector. (a.c)b-(a.c)c is scalar*vector minus scalar*vector. It's a vector. And you can just multiply it out.