39. Find an equation of the plane P in Figure 9. -Space 723 5 FIGURE 9 40. Verify that the plane x - y + 5z = 10 and the line r(t) = (1,0,1) + 1 (-2, 1, 1) intersect at P = (-3, 2, 3). In Exercises 41-44, find the intersection of the line and the plane. 41. x + y + z = 14, r(t) = (1, 1, 0) + t (0, 2, 4) 42. 2x + y = 3, r(t) =(2, -1, -1) +1(1, 2, -4) 43. z = 12, r(t) = t (-6, 9, 36) 44. x - z =6, r(t) = (1,0, -1) + t (4, 9, 2) In Exercises 45-50, find the trace of the plane in the given coordinate plane. 45. 3x - 9y + 4z =5, yz ? 46. 3x - 9y + 4z = 5, xz 47. 3x + 4z = -2, xy 48. 3x + 4z = -2, xz 49. -x + y= 4, xz 50. -x+y =4, yz 51. Does the plane x = 5 have a trace in the yz-plane? Explain. 52. Give equations for two distinct planes whose trace in the xy-plane has equation 4x + 3y = 8. 53. Give equations for two distinct planes whose trace in the yz-plane has equation y = 4z. 54. Find parametric equations for the line through Po = (3, -1, 1) perpen- dicular to the plane 3x + 5y - 7z = 29. 55. Find all planes in R3 whose intersection with the xz-plane is the line with equation 3x + 2z = 5. 56. Find all planes in R3 whose intersection with the xy-plane is the line r(t) = t (2, 1, 0). In Exercises 57-62, compute the angle between the two planes, defined as the angle 0 (between 0 and I ) between their normal vectors (Figure 10). 57. Planes with normals n1 = (1, 0, 1), n2 = (-1, 1, 1) 58. Planes with normals n1 = (1, 2, 1), n2 = (4, 1, 3) 59. 2x + 3y + 7z = 2 and 4x - 2y + 2z = 4 60. x - 3y + z =3 and 2x - 3z = 4 61. 3(x - 1) - 5y + 2(z - 12) = 0 and the plane with normal n= (1, 0, 1)