8. Determine the point of intersection of the three planes

₂x+3y-z+9-0

₂X-y+2-11-0

: [x, y, z] = [1, 0, 1] + s[2, 1, −1] + [4, 0, -1].

a. (1,-4,3)

b. (5,0,-5)

Communication [13 marks]

True/False

Indicate whether the statement is true or false.

9. A normal vector to a line is parallel to that line.

10. There is no symmetric form for the equation of a plane.

11. A plane written in scalar form can be written in vector form.

20.

12. In three-space there are two possibilities for the intersection of two lines.

13. A line will never intersect with a plane.

21.

Matching

Match the equation of each plane to its scalar form.

x-y-2z+4-0

A

D

B

2x-y-22-6-0

y-2 E

y-2-6-0

C

22.

c.

23.

d.

24.

(5,-4, 2)

(5, 11,-12)

x=3t+s

y-2-1-58

2=1+2+35

13x-7y+22+16-0

[x, y, z] = [3, 2, 1] + s[2, 0, 3] + t[3, 0, 2]

[x, y, z] = [5, -2, 3] + s[3, −2, 4] + t[5, -2, 6]

[x, y, z]= [5, 4, -2] + s[2, −1, −1] + t[1, 3, 3]

[x = -t+25

y-2-1+45

z=-1+3t+s