Plane and solid analytic geometry, by William F. Osgood and William C. Graustein.

THE PLANE

459

(X-2)+10 (y-5) + 7( + 8) =0,
or x+ 10y+ 7z+-4=0.
This is the required equation.
EXERCISES
In each of the following exercises find the equation of the
plane which is parallel to the given plane and passes through
the given point. In Exs. 5, 6 find the equation directly
by inspection of a figure.
Plane Point
1. 5x-2y+3z-4=0, (2, 4, 3).
2. 3x+4y-8z-2=0, (0, 0, 0).
3. 4x-2y-6z=9, (2,-1,0).
4. 3x-4z=0, (5, 2, -3).
5. 3x+8=0, (1 -2, 5).
6. 2y-5= 0, (4, 0, 3).
7. Find the equation of the plane passing through the
points (3, 1, 2), (3, 4, 4) and perpendicular to the plane
5 x + y + 4z= 0. Apply both methods, checking the result of
one by that of the other. Ans. 2x+2y -3 - 2= 0.
The previous problem, if the given points and the given
plane are as specified. Use either method in Exs. 8-10; in
Exs. 11, 12 solve the problem directly by inspection of a
figure.
Points Plane
8. (3,4,1), (2,6,-2), 2x- 3y+4z - 2 =0.
9. (0, 0, 0), (4, 3, 2), x+y +z=0.
10. (3, 2, - 4), (5, -, 3), 4 x - 5 = 8.
11. (1, 0, 0), (1, 2, 5), 3y- 7= 0.
12. (0, 2, 0), (2, 0, 0), 2z + 5 = 0.
13. There are infinitely many planes which pass through
the two points (2, - 3, 4), (- 2, 3, - 6) and are perpendicular