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