Elements of descriptive geometry, with applications to isometric projection and othe forms of one-plane projection; a text-book for colleges and ingineering schools by O. E. Randall.

RELATING TO POINT, LINE, AND) PLANE

63

171. Problem 109. Pass a plane through the point Q=- 2, - 6, 3
and parallel to the two lines [M= - 4, 5, - 3; L-= 4, - 3, 6] and
[O0=-2, -1, 5; P=6, -1, 5].
172. Problem 110. To pass a plane through a given point and
parallel to a given plane.
Analysis. The traces of the required plane will be parallel to
the corresponding traces of the given plane, and will be fully
known when one point in each trace is determined. A straight
line through the given point and parallel to either trace of the
given plane will be a line of
the required plane and will intersect H or V in the corre- s
sponding trace of the required \ \
plane. \ ma
Construction. In Fig. 73 let
S represent the given plane and \ b \T
let Mlrepresent the given point...
Through 3M draw M-A par- s. b
allel to S-s' and produce it to
meet H at a,. The point a, is
in the horizontal trace of the FIG. 73
required plane.
Through M3 draw M-B parallel to S-s, and produce it to meet
V at bV. The point b' is in the vertical trace of the required
plane.
The two required traces, T-t, and T-t', the former parallel to
S-s,, and the latter parallel to S-s', are now located.
Check. The two traces now determined should meet on G-L.
173. Problem 111. Pass a plane through the point M=-6,-4, -6
and parallel to the plane S=- 6, 40~, 60~.
174. Problem 112. Pass a plane through the point M=0, 3, 6
and parallel to the plane S = 0~, 5, 3.
175. Problem 113. To pass a plane through a given straight line
and parallel to another given straight line.
Analysis. Through any point of the first line draw a straight
line parallel to the second line. The plane of the first line and
the auxiliary line will be the required plane.