http://img84.imageshack.us/img84/1594/16233805.jpg

I'm not sure how to do part a) and b). For a) I don't get how the hint helps.

Eg, I did $\displaystyle P_1P_2 = \frac{1}{||a||^2}aa^T\frac{1}{||b||^2}bb^T$ and we know that a.b = 0 but there are no dot products in the former equation...

Cheers!