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21. The three planes with equations 3x y 7z 3 0,
4x 12y 4z 24 0, and x 2y 3z 4 0 do not simultaneously
intersect.
a. Considering the planes in pairs, determine the three lines of intersection.
b. Show that these three lines are parallel.
22. Solve for a, b, and c in the following system of equations:
2
a 2 5 b 2 3 1
c 2 40
3
a 2 6 b 2 1 2
c 2 3
9
a 2 5 b 2 4 3
c 2 67
23. Determine the equation of a parabola that has its axis parallel to the y-axis and
passes through the points 11, 22, 11, 12, and (2, 1). (Note that the general
form of the parabola that is parallel to the y-axis is y ax 2 bx c. )
24. A perpendicular line is drawn from point X13, 2, 52 to the plane
4x 5y z 9 0 and meets the plane at point M. Determine the
coordinates of M.
25. Determine the values of A, B, and C if the following is true:
11x 2 14x 9
13x 121x 2 12 A
3x 1 Bx C
x 2 1
(Hint: Simplify the right side by combining fractions and comparing numerators.)
26. A line L is drawn through point D, perpendicular to the line segment EF, and
meets EF at point J.
a. Determine an equation for the line containing the line segment EF.
b. Determine the coordinates of point J on EF.
c. Determine the area of ^DEF.
D(3, 0, 7)
F(–1, –4, –6)
J
L
E(4, 0, –3)
27. Determine the equation of the plane that passes through 15, 5, 52 and is
perpendicular to the line of intersection of the planes 3x 2z 1 0 and
4x 3y 7 0.
NEL
CHAPTER 9 555