Closest Point to a vector in a subspace Given v = [0 -3 -8 3], find the closest point to v in the subspace W spanned by [6 6 6 -1] and [6 5 -1 60]. This is web homework problem and I have used the formula (DotProduct(v, w.1)/DotProduct(w.1, w.1))*w.1 + (DotProduct(v, w.2)/DotProduct(w.2, w.2))*w.2 but the computer said the answer I got was wrong. If this isn't the formula than I'm not sure what is. I have triple checked my calculations as well. 
Any help would be greatly appreciated.

The projection of a vector $v$ over $\mathrm{span}(w_1, w_2)$ is the sum of the projections of $v$ over $w_1$ and $w_2$, if $w_1$ and $w_2$ are orthogonal. If they're not, you can find other vector that span the same subspace, using Gram-Schmidt's process. For example: $$\mathrm{proj}_{w_1} v = \frac{\langle v, w_1\rangle}{\langle w_1, w_1\rangle}w_1$$
The easy way to remember this formula is to think: if the projection goes in $w_1$'s direction, then it should be natural that $w_1$ appears the most in the formula. Think that $w_1$ guides $v$ through the right direction. Having this in mind, the exercise is just a calculation.
(also, I strongly suggest you look a bit about MathJax and LaTeX, so you can write formulas and stuff here right, otherwise, your question is not very visually appealing to people around here)
