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

THE PLANE

465

In each of the exercises that follow give all the information
you can concerning the relative positions of the three given
planes.
8x - 4y- 4z +=0, 9x + 6y-3z + 7=0,
9. -2x+ y+ z+5=0, 10. x-2y+ z+3=0,
6x-3y-3z-2=0. 6x+4y -2z-1=0.
11. 2x-3y+12=0, 3x+5y-1=0, 5x+2y+11=0.
12. 4x-3z-5=0, 3x+-5z-11=0, 7x+2z+3=0.
EXERCISES ON CHAPTER XIX
1. When will the plane Ax+By+ C~z+D = 0 pass through
a coordinate axis, e.g. the axis of z? When will it be parallel
to a coordinate axis, e.g. the axis of x?
2. Find the equation of the plane through the axis of z
and the point (1, 2, 0).
3. Find the equation of the plane through the axis of y and
the point (2, 3; 1).
4. What is the equation of the plane whose intercepts are
one half those of the plane 2 x - 3y + 4 z - 12 = 0?
5. A perpendicular from the origin meets a plane in the
point (2, - 3, 4). What is the equation of the plane?
6. A line through the point (2, 3, 7) meets a plane in the
point (5, - 1, 2). Find the equation of the plane.
7. Find the equation of the plane which bisects perpendicularly the line joining the points (4, 3, - 1), (2, 5, 3).
8. Determine the point on the axis of y which is equidistant from the points (3, 7, 4), (- 1, 1, 2).
9. One vertex O of a box is at the origin and the edges
issuing from 0 lie along the positive coordinate axes. Prove
that the intercepts of the plane which bisects perpendicularly
the diagonal through 0 are inversely proportional to the
lengths of the edges.