x =s+t 5. The parametric equations of a plane m: y = 1 + t. Find a scalar equation of the plane. Z =1-s a) x- y+z-2=0 b ) xty+z=0 c) x- y+z=0 d) x-y+z+2=0 6. Find the intersection point of the two lines: 11: { x = 5 - t ly = 4 - 2t and 12: * = 1 +s ly = -1+s a) (5, 4) b) (1 , - 1 ) C ) ( 4, 2 ) d) (1, 1) 7. In three-space, find the intersection point of the two lines: [x, y, z] = [3, 4, 0] + / [1, 1, 2] and [x, y, z] = [-1, 4, -20] + s [0, -1, 3]: a) (-1,0, -8) b ) ( 2 , 0 , - 3 ) c ) (-4 , -5, -8) d) (-4, -5, 1) x = 1+ 2t x = 2+3s 8. In three-space, find the intersection point of the two lines: y = -3 +t & y = -1+ 2s Z =-3 Z = S a) (1, -3, -3) b ) ( 2 , 1 , - 3 ) c) (2, - 1, 0) d) (-7 , -7, -3) 9. By analyzing the normals, determine if the two planes: m1: x+2y+3z-3=0 & 7 2: 2x - y + z - 7 = 0 a) intersect in a line b) are parallel and distinct c) are coincident d) intersect at a point 10. By analyzing the normals, determine if the three planes: m1: x + 2y + 3z - 4 = 0 & 12: 2x + 4y + 6z + 8 = 0 & 13: 4x + 8y+12z -10=0 a) intersect in a line b) are parallel and distinct c) are coincident d) intersect at a point