1. Oct 12, 2009

### phrygian

1. The problem statement, all variables and given/known data

Let x and y be vectos in R^n such that ||x|| = ||y|| = 1 and x^T * y = 0. Use Eq. (1) to show that ||x-y|| = sqrt(2).

2. Relevant equations

Eq. (1): ||x|| = sqrt(x^T * X)

3. The attempt at a solution

I could figure this out knowing that the dot product of the vectors is zero so the are perpendicular, the two sides of the triangle are 1 so the distance is sqrt(2) but this problem wants the answer to be found with Eq. (1) and I don't know how to do that and how to find ||x-y||.

Thanks for the help

2. Oct 12, 2009

### HallsofIvy

Staff Emeritus
Your formula says that ||x- y||= $\sqrt{(x- y)^T(x- y)}= \sqrt{x^Tx- x^Ty- y^Tx+ y^Ty}$. Both $x^Ty$ and $y^Tx$ are 0.