Find the the minimal distance from the point $P=(17, -19, 0)$ to the plane $V$ in $\Bbb R^3$ spanned by the vectors $u_1 = (4, -4, -2)$ and $u_2 = (-4, 1, 1)$.
So, I tried to apply the Best Approximation Theorem where the $\mathrm{dist}(P,W) = \| P - \mathrm{proj}_w P \|$ where $W = \mathrm{span} \{u_1, u_2\}$. But I realize that to apply the Best Approximation theorem $u_1$ and $u_2$ must be orthogonal and they are not.
So, to find an orthogonal basis for $W$ I used The Gram-Schmidt Process where I let $v_1 = u_1 =(4, -4, -2)$ and I obtained $v_2 = (-14/9, -13/9, -2/9)$. Hence, $\{v_1, v_2\}$ is an orthogonal set.
After this I tried to apply the Best Approximation Theorem to find the minimal distance but I still do not get the correct answer.
I hope my question makes sense.