1. The problem statement, all variables and given/known data 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? 2. Relevant 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 3. 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!