1. A line has slope - 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, y] = [-2, 0] +1 5,1 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 - 32 + 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] + t[3, -1, 4] and [x, y, z] = [-6, 8, -1] + 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] + t[4, 2, 0]. a. 1.79 units c. 2.67 units b. 3.14 units d. 1.03 units 5. Determine the distance between the lines r = (0, 1, -1) + s(3, 0, 1), SER with T = (0,0, 1) + t(1, 1, 0), tER 6. Find the intercepts of the plane 2x + 6y - 3z - 12 = 0.I Need full steps + answers written on papers. Please attach clean files. I need answers in about an hour. Thank you