Orthogonality and Inner Products: Understanding a Linear Algebra Proof

[Dustinsfl]

How to start this proof?

<u-p, p> = 0

 

[gabbagabbahey]

What are $\textbf{u}$ and $\textbf{p}$ supposed to represent? That statement isn't true for two general vectors $\textbf{u}$ and $\textbf{p}$.

What is the entire problem statement that you are given?

 

[Dustinsfl]

It has to do with inner product.

 

[Dustinsfl]

Is that equivalent to <u, p> - <p, p> = <u, p> - $$\left\|p\right\|$$²