Distance of a point from a plane Let \({\bf w}\in{\mathbb R}^3\). From your previous experience in geometry, all points \({\bf x}\in{\mathbb R}^3\) satisfying \({\bf w}^T{\bf x}=0\) form a ___ (fill up the blank).

What is the smallest possible distance of a point \({\bf z} \in {\mathbb R}^3\) from any point \({\bf x}\) satisfying \({\bf w}^T{\bf x} = 0\)?