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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] [x, y] = [-2, 0] +1 5,1 d. [x, y] = [-2, 0] + #[3, 2] 2. Write the scalar equation of the plane with normal vector n = [0, -1, 3] and passing through the point (5, -2, 3). a. y - 32 + 11 = 0 C. -y + 32 + 11 = 0 b. y - 32- 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] + t[3, -1, 4] and [x, y, z] = [-6, 8, -1] + 2[2, -5, -3]. a. (-1, 2, 0) C. (-4, 3, -4) b. (-6, 8, -1) d. (3, 2, 1) Determine the distance between the point (1, 0, 1) and the plane [x, y, z] = [1, 2, 3] + s[2, 1, 3] + t[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+1 a. 3.69 units C. 2.01 units b. 1.45 units d. 2.89 units x = 2+! x = 3+s+! 6. Determine the distance between the line {y = 5 - and the plane { y = 2-s -. 2 = -4 z = 1+s -! 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] + z[1, 0, 2]. a. 3.48 units c. 7.22 units b. 9.11 units d. 1.60 units