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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When the plane of the angle is revolved back to its original
position, d, will remain stationary and N will take its old position.
The horizontal projection of the bisector in true position will be at
n,-d, and its vertical projection will be at n'-d'.
Check. Revolve the plane of the angle about its vertical trace
into the vertical plane of projection.
143. Problem 81. Determine the angle between the two lines
[Mi=-6, 4, -2; N=O, -4, -6] and [N=0, -4, -6;
0 = 6, 2, 1].
144. Problem 82. Determine the angle between the two lines
[Mi=-4, 5, 6; N=4, 1, 2] and [N= 4, 1, 2; 0=4, 6, 2].
G at
f145FI. 64
145. Problem 83. Determine the angle between the two lines
[1fi=-4, -6, -6; Y= 4, -2, -2] and [N= 4, -2, -2;
0=4, -2, -5].
146. Problem 84. To find the intersection of two planes when
their traces are known.
CASE 1. When the horizontal traces of the two planes intersect
within the limits of the drawing and when the vertical traces of the
same planes also intersect within the limits of the drawing.
Analysis. The intersection of the horizontal traces must be a
point common to both planes and therefore a point in their intersection. For the same reason the intersection of the vertical traces
must be another point in the required intersection.