Proving the Lagrange Triple Vector Identity for Orthogonal Coordinates

[asd1249jf]

Homework Statement

Prove

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

For orthagonal coordinates, a,b,c

Homework Equations

Cross Product and Dot Product

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?

 

[asd1249jf]

I should clarify a bit

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

 

[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.