Finding a projection

Question

Could someone please explain how to find a projection on to a vector of a subspace?

for example: I need to find the projection onto $v = {(2,3,0)}$ of $U = \text{sp} \{(1,1,1),(1,2,3)\}$

much appreciation, Tom

Answer 1

Hint:

If you are finding a projection of $U$ onto $v$ is enough to project $u=(1,1,1)$ and $w=(1,2,3)$ onto $v=(2,3,0)$.

In general, an orthogonal projection of $u$ onto $v$ is given by:

$$p=\left(\frac{u\cdot v}{|v|^2}\right)\cdot v$$

P.S: Can you finish from here?