Which of the following pairs of lines are perpendicular? (a) 3x - 5y = 1 and 2x + y = 2 (b) 2x + 7y = 1 and x - y = 5 (c) 3x - 5y = 1 and 5x + 3y = 7 (d) -x + y = 2 and x + y = 9 find the equation of the plane perpendicular to the given vector n and passing through the given point p. (a) n = (1, -1, 3), p = (4, 2, -1) (b) n = (-3, -2, 4), p = (2, pi, -5) (c) n = (-1, 0, 5), p = (2, 3, 7) find the equation of the plane passing through the following three points. (2, 1, 1). (3, -1, 1), (4, 1. - 1) (b) (-2, 3, -1), (2, 2, 3), (-4, -1, 1) (-5, -1, 2), (1, 2, -1), (3, -1, 2) find a vector perpendicular to (1, 2, -3) and (2, -1, 3) and another vector perpendicular to (-1, 3, 2) and (2, 1, 1). find a vector parallel to the line of intersection of the two planes 2x - y + z = 1. 3x + y + z = 2. same question for the planes. 2x + y + 5z = 2, 3x - 2y + z = 3. find a parametric representation for the line of intersection of the planes of exercises 10 and 11. find the cosine of the angle between the following planes: (a) x + y + z = 1 x - y -z = 5 (b) 2x + 3y - z = 2 x - y + z = 1 (c) x + 2y - z = 1 -x + 3y + z = 2 (d) 2x + y + z = 3 -x - y + z = pi (a) let p = (1, 3, 5) and a = (-2, l, l) find the intersection of the line through p in the direction of a. and the plane 2x + 3y - z = 1. let p = (1, 2, 1). find the point of intersection of the plane 3x - 4y + x = 2, with the line through p. perpendicular to that plane. let q = (l, -1, 2) p = (1, 3, -2) and n = (1.2.2). find the point of the intersection of the line through p in the direction of n. and the plane through q perpendicular to n. find the distance between the indicated point and plane. (1, 1, 2) and 3x + y - 5z = 2 (-1, 3, 2) and 2x - 4y + z = 1 (c) (3. -2, 1) and the yz-plane (d) (-3, -2, 1) and the yz-plane