Knowledge/Understanding Multiple Choice: [10 Marks] 1. A link passes laugh the points A (7, -4)4 B (-5, -2). Find a value equation uf'the line. a) [x. y] = [7,-4) + +[-5,-2] b) [x. y] = [7,-4] + 2[-2,-6] c) [x. y] = [-5.-2] + ([-12,2] d) [x. y] = [12,-2] + 4[7,4] 2. A line has slope -3 and x-intercept 5. Find a vector equation of the line. a) [x. yl = [-3, 1] + +[5, 0] b) [x.y] = [0,5] + ([-3,1] c) [x. y] = [5,0] + 4[-1,3] d) [x-y] = [-1,-3] + ([0,5] 3. Write the scalar equation of the plane with normal vector ni = [3, 2, 1] and passing through the point (4, 5, 6). a) 3x + 2y +2 - 28 = 0 b) 4x + 5y + 62 + 28 = 0 c) 3x + 2y + 2+ 28 = 0 d) 4x + 5y + 62 - 28 =0 4. A plane passes through the origin and has the direction vectors [-1, -2, -3] and [-1, 3, -2]- Find a scalar equation of the plane. 2) -1 - 2y - 32 = 0 bj 13x+ y - 52 = 0 c) -x+ 3y - 2z =0 d) 5y +2=0 1 OVS - MCV4U 5. The parametric equations of a plane : y = 1 + f. Find a scalar equation of the plane. 1=1-$ a) x-y+2-2=0 bj Ity+z=0 ( x-y+2=0 d) x-y+z+2=0 6. Find the intersection point of the two lines: (1: *= 5- by =4- 2 and 12: * =1+; ly= -1+s ) (5.4) bj (1, -1) c) (4,2) d) (1, 1) 7. In three-space, find the intersection point of the two lines [x, y, =] - [3, 4, 0] + + [1, 1, 2] and [x, y. =] - [-1, 4, -20] + s [0, -1, 3]: 2) (-1,0.-8) bj (2,0. -3) c) (-4.-5, -8) d) (-4,-5,1) :=1+2 * = 2+3s 8. In three-space, find the intersection point of the two lines (y = -3 +t & y=-1+2: 1= -3 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: n: x+ 2y+ 32 - 3=0 & 12:2x- y+2-7=0 a) intersect in a line bj are parallel and distinct c) are coincident dj intersect at a point 10. By analyzing the normals, determine if the three planes: "j'"+7y+3-4=0 & nor+dy+63+8=0&s Ar+Ry +129 - 10=0 a) intersect in a line b) are parallel and distinct J indussul al a pusud