With the cross-product of a 3-dimensional space, how do you find the scalar product with a specific solution?

Question

In R^3 x R^3 x R^3 , how do I show that for all a, b,c element of R^3 the scalar product of 1) and 2) equations result in the specific end result given?

1. <a, a x b>= 0

2. a x (bxc) = b <a,c> - c<a,b>

Is it right to...

1. Find the cross product of a and b =c
2. Find cross product of a and c and then a little clueless on how I would get to the end end line. Any direction would be appreciated!