# How to prove this without computation

1. Apr 12, 2015

### Loststudent22

1. The problem statement, all variables and given/known data
Prove: In R3if a and b are orthogonal vectors, then for every nonzero vector u, we have proja(projbu)=0

2. Relevant equations
I know the dot product of a and b is zero

3. The attempt at a solution

Based on the definition of projection I eventually got to
(ab) in the numerator which is zero and was done. So how can I write this out with words only?

2. Apr 12, 2015

### LCKurtz

You haven't defined projbu but I suppose it is the projection on b of u. I'm not sure why you want to write it "in words" instead of equations, but you could observe that the projection on b of u is a multiple of b. Then since a is orthogonal to b, then....

3. Apr 12, 2015

### Loststudent22

then that component is zero? Yeah I will add the computation also but I wasn't really sure what else to say.

yeah its the projection on b of u