1) [2K] Determine the distance between the point P(2, -5) and the line L: 7 = (-4,0) + 1(2,3), te R. 2) [2K] Determine whether r = -1, y =3 and 2 = 5 is a solution to the system: a) 4x - 2y + 2=-5 b) z +3y - 2: =7 3) [6C] Describe 4 of the 6 possible ways in which 3 planes can interact. Draw diagrams to help you. How many solutions does each case give? 1) Complete the following questions using the following planes: m : 2x + 4y - 62 = 2 12 : 7x - y = 7 #3 : 4x + 8y - 112 = -1 a) [2K] Determine the normals to each plane. b) [3C] Are any of the planes parallel? Explain. c) [6A] Determine the solution(s) to the system of equations AND describe the way in which these planes intersect (or dont intersect). d) [2K] Let m, be a fourth plane that passes through the points A(2, 0, -1), B(2, 1, 1) and C(-3, 4, 2). Find the Cartesian equation of 4- e) [3A] Find the intersection of m and *4 (if it exists). f) [3A] Find the distance between as and is : 8x + 16y - 22: = 5. g) [2K] Find the angle between $2 and *3- 5) [2K] Determine the points of intersection between the line L : 7 = (1,0,2) + t(3, -1,0), t E R and the plane * : 3x - y + 22 = 4 if any exist. 6) [6T] If mix+y+ = =0 and *2 : x+ 2y + 22 - 1 =0 intersect at a line that lies on the plane #3 : 2x - y + mz + 3 =0. Find m. 7) [6T] A plane *2 intersects *: 4x - 2y + 72 - 3=0 at right angles. Two points lie on 2: (3, 2, 0) and B(2, -2, 1). Write a Cartesian equation for $2