Consider the line L in R 3 , given by x = -λ + 2, y = 2λ - 1, and z = λ + 3 where λ ∈ R.
(a) Verify that the point (2, -1, 3) lies on L, but that (1, 1, 1) does not.
(b) Find the cartesian equation for the plane P, containing (2, -1, 3), that is orthogonal to L.