Some linear algebra love?

[Anonymous No.8944646]

How does one prove that if [math]\vec{q}=\vec{b}-\vec{p}[/math] where [math]\vec p\in{U}[/math] is the orthogonal projection of [math]\vec{b}\in{V}[/math],then [math]\vec{q}\bot\vec{p}[/math]?

[Anonymous No.8944651]

Are you seriously asking for high-school homework advice?

[Anonymous No.8944659]

>>8944646
Let ^p = p/|p|

p=|^p*b| ^p
p*q=p*b-p*p = |^p*b| ^p*b -|^p*b|^2 = 0

[Anonymous No.8944668]

>>8944659
Is * the dot product?