Transitive Property with Orthogonal Vectors?

[georgetown13]

Homework Statement

Let x1, x2, and x3 be vectors in R^3. If x1 is orthogonal to x2 and x2 is orthogonal to x3, is it necessarily true that x1 is orthogonal to x3?

Homework Equations

I know that if x1 is orthogonal to x2 and x2 is orthogonal to x3, then...

(x1)^T*x2=0
(x2)^T*x3=0

The Attempt at a Solution

I think that the answer would be no. I can imagine it geometrically, but I'm not sure how I would prove this algebraically.

I would obviously have to prove that (x1)^T*x3 would ALWAYS have to equal 0 if it the statement was necessarily true... but I'm not sure how to go about doing that...

I'm completely stuck. I would greatly appreciate your help!

 

[radou]

Try to think of an example.