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.

58

DESCRIPTIVE GEOMETRY

For ease of construction let us take the horizontal projecting
plane of iM-N as the auxiliary plane. This plane ' intersects S in
A-B (see Section 146), wlich is cut by AM-N at the required point D.
Check. Use the vertical projecting plane of iM-V.
CASE 2. When the given plane is located by two intersecting
straight lines.
Construction. See Fig. 68. Let Jl-zV and O-P, intersecting at L,
locate the given plane, and let Q-R represent the intersecting line.
By Case 1 above, M-N intersects the horizontal projecting plane
of Q-R at A. O-P intersects the same plane at B. Therefore A-B
is the intersection of the
horizontal projecting
1 ---fi^-q.^ n < plane of Q-R and the!:??"ba r e plane of the two given, i l,.:-,,1in lines /l-NV and O-P.
>.1' -," - La 'L Q-R crosses A-B at D,, //:, which by analysis is,3\:: >:: "the required point of: \j:N / '-4,: intersection.:! ^^ ^^^y?, Check. Use the ver^/u ^r' tical projecting plane of
'r''\ Q-R.
FIG. (8 152. Problem 90. Find
the point in which the plane determined by the two lines [1 = - 6,
6, 6; Y= 0, 2, 1] and [M=- 6, 6, 6; 0 = 2, 8, 4] is intersected
by the line [Q = - 4, 2, 2; R = 2, 6, 8].
153. Problem 91. Find the point in which the plane determined by
the two lines [M = - 4, - 2, - 8; N = - 4, - 8, - 2] and [A = - 4,
- 2, -.8; 0 = 4, - 7, - 3] is intersected by the line [Q =- 6, - 6,
-2; R= 6, -6, -8].
154. Problem 92. To draw through a given point a straight line
perpendicular to a given plane, and to determine the distance of the
point from the plane.
Analysis. By Section 44 we know that the horizontal projection
of the required line must be perpendicular to the horizontal trace
of the given plane, and that the vertical projection of the required
line must be perpendicular to the vertical trace.