Find the minimal distance from the point $P = \begin{bmatrix}\\ -8 \\ 14 \\ 8 \end{bmatrix}$ to the plane $V$ of $\mathcal{R}^3$ spanned by $\begin{bmatrix}\\ 1 \\ 2 \\ -2 \end{bmatrix}$ and $\begin{bmatrix}\\ 6 \\ -5 \\ -2 \end{bmatrix}$.
How would I compute this?
Hint: See the picture below and don't forget to normalize the normal. What are the coordinates of the closest point?