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

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164. Problem 102. Project the line [M = - 4, - 4, - 4; N = 0,
- 8, - 6] upon the plane S = - 6, 315~, 330~, following Analysis 2.
165. Problem 103. To pass a plane through a given point and
perpendicular to a given straight line.
Analysis. From Section 44 we know that the horizontal and
vertical traces of the required plane will be perpendicular respectively to the horizontal and vertical projections of the given line.
We know, then, the direction of each of the required traces. If a
straight line be drawn through the given point parallel to either
of these traces, it must be a line of the required plane, and, unless
parallel to G-L, will intersect one of the planes of projection in
a point of the corresponding trace of the required plane. A
straight line through the point thus found and perpendicular
to the corresponding projection of
the given line will be one of the
required traces.
The other required trace will pass ~s,
through the point in which the trace
just found intersects G-L, and will G- m S
be perpendicular to the remaining \ I /
projection of the given line. o0
Construction. See Fig. 71. Let
M-N represent the given line, and
let 0 represent the given point.
Through 0 draw 0-A parallel to the
horizontal trace of the required plane. FIG. 71
Since this horizontal trace is to be perpendicular to m,-n,, the
horizontal projection of O-A will be perpendicular to m,-n,.
Since O-A is parallel to a line in H, its vertical projection will
be parallel to G-L.
The point a' in which O-A intersects V is a point in the vertical
trace of the required plane, and S-s' drawn through a' perpendicular to mt-n' is the required vertical trace. S-s, drawn through
S perpendicular to m,-n, is the required horizontal trace.
Check. Draw a line through O parallel to the required vertical
trace, and note whether such a line intersects H in the horizontal
trace already found.