Knowledge / Understanding [8 marks] Identify the choice that best completes the statement or answers the question. 1. A line has slope 5 and x-intercept -2. Find a vector equation of the line. a. [x, y] = [3, 2] + #[-2, 0] c. [x, y] = [-2, 0] + *[2, 3] b . [x, x] = [-2, 0] + + 3.1 d. [x, y] = [-2, 0] + #[3, 2] 2. Write the scalar equation of the plane with normal vector / = [0, -1, 3] and passing through the point (5, -2, 3). a. y - 3z + 11 = 0 c. -y+ 32 + 11 = 0 b. y- 3z - 11 = 0 d. -y+ 32 + 16 = 0 3. In three-space, find the intersection point of the two lines: [x, y, z] = [-1, 2, 0] + #[3, -1, 4] and [x, y, z] = [-6, 8, -1] + ([2, -5, -3]. a. (-1, 2, 0) C. (-4, 3, -4) b. (-6, 8, -1) d. (3, 2, 1) 4. Determine the distance between the point (1, 0, 1) and the plane [x, y, z] = [1, 2, 3] + s[2, 1, 3] + ([4, 2, 0]. a. 1.79 units c. 2.67 units b. 3.14 units d. 1.03 units x = 1+t 5. Determine the distance between the point (4, 3, 2) and the plane {y = 2 + s z = 3+5+ a. 3.69 units C. 2.01 units b. 1.45 units d. 2.89 units x = 2+t x =3+5+! 6. Determine the distance between the line {y = 5 - and the plane { y = 2-s-t. Z =-4 z = 1+s-t a. 2.33 units C. 1.41 units b. 5.12 units d. 0.34 units 7. Determine the distance between the line [x, y, z] = [4, 5, -2] + f[1, 1, -1] and the plane [x, y, z] = [2, 4, 3] + s[3, 2, 0] + t[1, 0, 2]. a. 3.48 units C. 7.22 units b. 9.11 units d. 1.60 unitsPage 2 of 6 8. Determine the point of intersection of the three planes :1: x+ 3y-z+ 9 = I] x2:xy+z11=U '53: [x3 y! Z] = [1) 0) 11+ 512,1: _l] + 4:4) 0: _1]' a. (1,4, 3) c. (5,4, 2) b. (5,0,5) d. (5,11,12)