Let W be the line with parametric equations x = 2t, y = - t, z =

Question:

Let W be the line with parametric equations
x = 2t, y = - t, z = 4t (- ∞ < t < ∞)
(a) Find a basis for W.
(b) Use Formula 6 to find the standard matrix for the orthogonal projection onto W.
(c) Use the matrix obtained in (b) to find the orthogonal projection of a point P0(x0,y0,z0- zo) onto W
(d) Find the distance between the point P0(2, 1,-3) and the line W.