Find the equation of the plane orthogonal to the line L and passing through P, where L:{x = 4 + t y = 1 - 2t (t epsilon R) z = 8t and P(2, 3, 1) Find the distance between the point Q(2, 0, 1) and the plane pi: -4x + y - z + 5 = 0 Given three nonzero vectors u, v and w in R^n, if the angle between u and w is equal to the angle between v and w, show that w is orthogonal to the vector ||v|| u - ||u||v Use Cauchy-Schwarz inequality to prove that if a_1 and a_2 are nonnegative real numbers, then Squareroot a_1 a_2 lessthanorequalto a_1 + a_2/2.
