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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In this way the problem is solved by a method which in theory
is the same as that explained above, but which in application is
entirely independent of it.
In the above problem, if one of the two given lines is perpendicular to the plane of projection, the required line will be parallel
to the plane of projection, and its own projection will pass through
the point projection of the line which is perpendicular to the plane
and will be perpendicular to the projection of the other given line.
If one of the two given lines is parallel to the plane of projection,
the projection of the required line upon this plane will be perpendicular to the projection of the parallel line upon this plane.
200. Problem 138. Given the two straight lines [M= - 5, 3, 5;
n = 5, 3, 5] and [O = - 4, 2, 6; P =4, -4, -3]; required the
projections of the straight line perpendicular to both.
201. Problem 139. Given the two straight lines [M=- 5, 3, 5;
N=5, 3, 5] and [0=2, - 6, 7; P = 2, 1, -6]; required the
projections of the straight line perpendicular to both.
202. Problem 140. Given the two straight lines [M=- 5, - 6,
-6; N= 3, 1, - 2] and [O = - 4, - 6, - 3; P = 4, -7, - 6];
required the shortest distance between the two lines.