Find the minimal distance from the point $(8,−2,−6)$ to the plane $V$ in $\Bbb R^3$ spanned by $\langle -2,-2,2 \rangle$ and $\langle 2,1,1\rangle$.
We know that in order for vectors to be orthogonal their dot product must equal to $0$. Since your vectors aren't orthogonal you can use Gram Schmidt process to orthogonalize the given vectors. Once you use that method, then you can use projections to find the minimum distance. If you need me to elaborate any further just ask.