# Thread: Proof question - Orthogonal Vectors

1. ## Proof question - Orthogonal Vectors

I can never seem to prove these things. I have a practice question and I'm not sure how the layout should be.

Suppose a vector y is orthogonal to vectors u and v. Show that y is orthogonal to the vector u+v.

I know the basic rules for what makes vectors orthogonal but when I have to generalise that to show stuff like this i get totally lost. Any help please?

2. $\displaystyle <y,u+v>=<y,u>+<y,v>=0+0=0$

3. Ok, I am not sure i understand what you mean by <y,u>? is this the coordinate representation of a vector?

4. Originally Posted by Ife
Ok, I am not sure i understand what you mean by <y,u>? is this the coordinate representation of a vector?

It is one of the notations for the inner product: $\displaystyle <y,u>=y\cdot u=(y|u)$ etc.

5. you may know <y,u> as the "dot product".

6. ohh. i haven't seen it like that as yet, i think.. thanks

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# suppose a vector y is orthogonal to vectors u and v. show that y is orthogonal to the vector u v

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