We have a point(3,3,3) in R3, and a plane not going through origin. Now if I wish to find a distance from the plane to the point, I could not just do the usual stuff: project $\begin{bmatrix} 3 \\ 3\\3\end{bmatrix}$ onto the normal of the plane, and find the length of it, because the vector $\begin{bmatrix} 3 \\ 3\\3\end{bmatrix}$ is not useful here since it goes from the origin to the point (3,3,3). Am I right, and what could be my course of action?
Thank you!
Let $a=(3,3,3)^T$.
Find a point $x$ that lies on the plane.
Compute $a-x$, then you can project it onto the normal of the plane and find the length.