Let S be the oriented surface F(u,v) := (5u2 + 2v, 4v² + 4u, 5u + 3v), 0

Consider a point Q(x1, y1, z1) and a line L given by the vector equation r = r0 +tv,where r0 = <x0, y0, z0> and v = <a, b, c>. Prove that the distance d from the point Q to the line L isd = |v × <x1 − x0, y1 − y0, z1 − z0>|/|v|.

Let L be the line passing through the point P(1, −1, −2) with direction vector d=[3, −4, 0]T, and let T be the plane defined by −3x+3y-2z = -8. Find the point Q where L and T intersect. Q=(0, 0, 0)

Let L be the line passing through the point P(−1, 1, 5) with direction vector d=[4, −1, 0]T, and let T be the plane defined by 5x+y-2z = 25. Find the point Q where L and T' intersect. Q=(0, 0, 0)