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

THE STRAIGHT LINE

495

Show that the first of the two following lines intersects the
axis of z and that the second intersects the axis of x.
(2x+3y- z+2=0, x -4 42y+63 6 3z+4
j x-2y+2z-4=0. 5 4 3 2
6. What is the condition that the line
Aix + Bly + Clz + D1 = O, A2x+ B2y + Cz + D2 = 0,
where C1C2 # 0, meet the axis of z? Ans. C1D2 - C2D = O.
Show that the following lines are identical.
2x + y-sz 5 +2,=0, r4xa+y-8z+3- 0,
* 6x- -2y —5z+-l=0; [2x-2y+z-l=O.
8. x q- y - -z + I =O, 0 '2x-2y~z=1=0
jx+Y-Z+1=O, X+Il1-=1y
12x+3y —1=0; 3 2
9. Find the equations of the altitudes of the tetrahedron of
Ch. XIX, ~ 6, Ex. 9.
10. Find the equation of the plane which contains the point
(2, - 1, 5), is perpendicular to the plane 2 x - y + 3z = 4, and
is parallel to the line
5x + 2y + 3z =0, 4x +y+2z-8 = 0.
Ans. 3x —9y —5z+10=0.
11. Find the equation of the plane which passes through the
points (2, - 1, 3), (5, 0, 2) and is parallel to the line
2 x - 5 - y = 2- 3 z.
12. Find the equations of the line which contains the point
(4 2, - 3), is parallel to the plane x + y + z = 0, and is perpendicular to the line whose equations are x - 2y - z = 5,
z = 4. Ans. 6x-24 = 3y-6=-2z-6.
13. A line is parallel to the plane 2 x - 3 y 4 = 0. If the
perpendicular from the origin on the line meets it in the point
(2, 5, - 3), what are the equations of the line?
14. Show that the equation of the plane which passes
through the point (x0, y,, z0) and is parallel to two (non-parallel)