8 determine the point of intersection of the three planes x 3y z 9 0 x
8. Determine the point of intersection of the three planes
: [x, y, z] = [1, 0, 1] + s[2, 1, −1] + [4, 0, -1].
Communication [13 marks]
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.
12. In three-space there are two possibilities for the intersection of two lines.
13. A line will never intersect with a plane.
Match the equation of each plane to its scalar form.
[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
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