Find the orthogonal projection of the given vector on the given subspace $W$ of the inner product space $V$.

Question

$V=\mathbb R^2,u=(2,6), $ and $W={\{(x,y):y=4x}\}$.

I've no idea about how to get through this. Please help in understanding this in detail,if possible pictorial representation will be best.

Answer 1

Hint : You have that the vectors in W are written as $(x,4x) \Leftrightarrow x(1,4)$ That means that every vector in W is a linear combination of $(1,4)$ which is mathematically written as $ W= span[(1,4)]$. From this, you should be able to easily find what you asked.

Answer 2

Thanks Charalampos Filippatos for the hint.