1) For the line that passes through the points A{5, 8, -2) and B(-1, 3. 5), nd a) a vector equation. (K 2 marks} 13} parametric equations. (K l' mark} 2) Determine if and how the following lines intersect. If they intersect at a single point, find the point of intersection. (K - 4' marks) 3) Determine if and how the following line and plane intersect. If they intersect at a single point, determine the point ofintersection. (K 3 marks) Line: (any, :) = (4, -2, 3) + {(-1, 0, 9) Plane: 4x 3y :+ '3' = 0 4) The lines {x,y, :) = {3,8, 1) + 3(1, 1,1) and {x,y,:) = (1,4,2) + III3,173) intersect at a point. a) Determine the value of k. {A 2 marks) 13) Determine the coordinates of the point of intersection. (A 3 marks) 5} For each of the following sets of three planes, determine {by inspection) which diagram describes the intersection of the planes. Write the corresponding letter in the blank space provided. {A 5 marks) E1: E2: E3: E1: E2: :13: El: E2: E3: in: E2: E3: in: E2: E3: x+2y+3:4=U 3x+6y+9:12={] 5x+lUy+lSz20=U x+2y+3:4=U 3x+6y+9:ll= 5x+10y+15:16=0 x+2y+3:4=U 3x+6y+9:12={] 5x+10y+15:16=U x+2y+3:4=U 3x+6y+9:12={] 3x+5y22l=0 x+2y+3:4=U 3x+6y+9zll=0 3x+5y22l=0 \"Z7 6) A plane contains the points A(5, -2, 9), B(-3, 0, 6) and CM, 1, -2). a) Find a vector equation for the plane. [I 3 marks) b} Find a scalar equation for the plane. [I 3 marks) 7) Determine if and how the following planes intersect. If they intersect along a line, nd the parametric equations of the line of intersection. (I 4 marks) m:3xy+4:7=U Irzzx+y22+5:U 8} Determine if and how the following planes intersect. If they intersect at a single point, determine the point of intersection. If they intersect along a single line, nd the parametric equations of the line of intersection. Otherwise, just state the nature of the intersection. (C .5 marks) m: 3x3y2zl420 E2: 5x+y6:l:0 1:3: x2y+4z9=U