In R4\mathbb{R}^4R4, let WWW be the plane spanned by
w1=(1, 1, 1, 1),w2=(1, 3, −1, 1)\mathbf{w}_1 = (1,\ 1,\ 1,\ 1), \qquad \mathbf{w}_2 = (1,\ 3,\ -1,\ 1)w1=(1, 1, 1, 1),w2=(1, 3, −1, 1)
and let
v=(5, 3, 1, 3)\mathbf{v} = (5,\ 3,\ 1,\ 3)v=(5, 3, 1, 3)
The distance from v\mathbf{v}v to WWW is minp∈W∥v−p∥\min_{\mathbf{p} \in W}\|\mathbf{v} - \mathbf{p}\|minp∈W∥v−p∥, the length of the shortest path from v\mathbf{v}v to any point of the plane.
What is that distance?
Select all that apply.
222\sqrt{2}22
666
38\sqrt{38}38
6\sqrt{6}6