8 determine the point of intersection of the three planes x 3y z 9 0 x

Question

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