Linear algebra involving dot product and orthongal matrices

[ItsKP]

Homework Statement

Given: x (dot) y = x^T * y (where x,y are vectors; dot is dot product; and x^T is x transpose)
and R is an orthogonal nxn matrix, and x,y are elements of R^n

Show ||Rx|| = ||x||

The Attempt at a Solution

I'm not sure what information I am suppose to use to solve this. This is what I have gathered so far:
x(dot)y = x1y1 + x2y2+ ... + xnyn = x^T * y

But how am I suppose to use any of this to solve the problem? Is it involving inner products at all?

 

[arkajad]

I'm not sure what information I am suppose to use to solve this.

The crucial information is that R is an orthogonal matrix: R^TR=RR^T=Identity matrix.