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

DIRECTION COMPONENTS

433

EXERCISES
In each of the following exercises find all the sets of direction components of the given line and then choose from them
a simple set.
1. A line parallel to the axis of x.
2. The line bisecting the angle between the positive axis
of x and the negative axis of z.
3. A line in the (x, y)-plane having the slope 2.
Ans. p, 2p, 0; 1, 2, 0.
4. A line in the (y, z)-plane making an angle of 60~ with
the y-axis. Two answers.
5. A line making equal angles with the three coordinate
axes.
6. The line through the origin and the point (2, 1, 3).
7. The line through the points (2, 3, 5), (4, 7, 8).
8. What can you say of the position of a line if one of its
direction components is zero? If two are zero?
In each of the following exercises construct the line through
the given point with the given direction components.
Point Direction Components
9. Origin, 3, 5, 2.
10. Origin, 2, - 3, 6.
11. (2, 4, 3), p, p, 2p (p 0).
12. (5, -4, 6), 3, 0, -1.
13. (2, 5, - 3), 0, 1, 0.
4. Formulas for the Use of Direction Components. Direction
Components of the Line through Two Points. Let the two points
P1: (x1, Y, Zl), P2: (2, Y2, z2) be given. Since the projections of
PiP2 on the axes are (Ch. XVII, ~ 6),
(1) X2-X, Y2 - Y1, Z2- Zi