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 $\langle 2,1,1\rangle$.
- Anybody can ask a question
- Anybody can answer
- The best answers are voted up and rise to the top
The technique is to find the equation of the plane $ ax+by+cz+d=0 $, then use the formula of the distance
For more details see here.
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.