# Are two vectors that are orthogonal to a third parallel?

1. Jan 19, 2017

### Vitani11

1. The problem statement, all variables and given/known data
Is it true in three dimensions that any two vectors perpendicular to a third one are parallel to each other?

2. Relevant equations
Dot product.

3. The attempt at a solution
I've come up with two vectors that were orthogonal to a third and found the angle between them using the definition of the dot product and the angle was not 180 degrees. Therefore I don't think that it's true. I'm really only here to check that I did my math right. Is it actually not true, or do I need to recalculate?

2. Jan 19, 2017

### vela

Staff Emeritus
You're probably overthinking the problem. You should be able to easily come up with a counterexample which shows the statement is false.

3. Jan 19, 2017

### VrhoZna

Not in general, consider the dot products of two non-parallel vectors with the 0 vector.

4. Jan 19, 2017

### StoneTemplePython

If you want something visual, you might ponder the right hand rule...

5. Jan 19, 2017

### Eclair_de_XII

In my opinion, you should try computing the cross product of two parallel vectors, since the cross product produces a vector normal to both those vectors. Can you do it? If you can answer that question, then you can answer the original question, I think. Given you know how to cross-multiply vectors. But since you're given only the definition of the dot product, you can kindly disregard this post.

Last edited: Jan 19, 2017
6. Jan 20, 2017

XYZ axes?