Question

# 2 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] d. [x, y]-[-2,0]+[3,2] b. (x,y) = (-2.0) + [ 3.1 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 b. y-3z-11-0 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) b. (-6, 8,-1) c. -y+32+11-0 d. -y+32+ 16-0 4. Determine the distance between the point (1, 0, 1) and the plane [x, y, 2] = [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 a. 3.69 units b. 1.45 units c. (-4,3,-4) d. (3, 2, 1) x=1+t 5. Determine the distance between the point (4, 3, 2) and the planey - 2+s z=3+5+1 a. 2.33 units b. 5.12 units c. 2.01 units d. 2.89 units x=2+t [x=3+5+1 6. Determine the distance between the line y-5- and the planey-2-s-t. z=1+8-t c. 1.41 units d. 0.34 units 7. Determine the distance between the line [x, y, z] = [4, 5, −2] + [1, 1,-1] and the plane [x, y, z] = [2, 4, 3] + s[3,2,0] + [[1, 0, 2]. a. 3.48 units b. 9.11 units c. 7.22 units d. 1.60 units  Fig: 1