How to prove this without computation

[Loststudent22]

Homework Statement

Prove: In R³if a and b are orthogonal vectors, then for every nonzero vector u, we have proj_a(proj_bu)=0

Homework Equations

I know the dot product of a and b is zero

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? [/B]

 

[LCKurtz]

Homework Statement

Prove: In R³if a and b are orthogonal vectors, then for every nonzero vector u, we have proj_a(proj_bu)=0

Homework Equations

I know the dot product of a and b is zero

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? [/B]

You haven't defined proj_bu 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...

 

[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