Consider the line l in R^³ given parametrically by x = x₀ + ta. Let P₀ denote the plane through the origin with normal vector a (so it is orthogonal to l).

a. Show that l and P₀ intersect in the point x₀ - proj_ax_0.

b. Conclude that the distance from the origin to l is||x₀ - proj_ax₀||.