Can anyone help? I am really stuck on this question.
Find the orthogonal projection of $(49 \ \ 49 \ \ 49 )^T$ on to the subspace $V$ of $R^3$ spanned by $(2 \ \ 3 \ \ 6)^T$ and $(3 \ -6 \ \ 2)^T $
(Sorry I don't know how to format matrices into the question. They are just meant to be stacked $3 \times 1 \ $ matrices.)
First you can get a vector orthogonal to that plane by forming the cross product $n$ of $(2,3,6)$ and $(3,-6,2).$ Next, if you form $P(k)=-(49,49,49)+kn,$ that vector starts at $(49,49,49)$ and is orthogonal to the plane. Only thing left now is to find what $k$ value makes $P(k)$ end up on the plane, plug in. I'll leave the last part for you... Note I changed the sign on $P(k)$ [which makes no real difference, but makes it as a vector start at $(49,49,49)$]