Answer to Question #210419 in Linear Algebra for Ree

Question

3.1) Find an expression for 1 2||u + v||2 + 1 2||u −v||2 in terms of ||u||2 + ||v||2.

(3.2)Find an expression for ||u + v||2 − ||u −v||2 in terms of u ·v

(3.3) Use the result of (3.2) to deduce an expression for ||u +v||2 whenever u and v are orthogonal to each other.