You will need

- - pencil;
- - notebook;
- - handle.

Instruction

1

Carefully read the conditions of the job: how you will understand it, depends largely on the final result.

2

To construct the line of intersection of two planes find two common points of these planes that will continue to draw a straight line. Note that given a triangle ABC the plane may be represented by straight lines (AB), (AC), (AF). The point where line (AB) intersects with the plane a', label D, and direct (AC) what was the point F. Thus, the segment (DF) will determine the line of intersection of these two planes. Due to the fact that a is the horizontally projected plane, the projection of the line segment D1F1 will coincide with the trace of the plane AP1. Hence, it appears that you only need to build the missing projection line (DF) on the planes P2 and P3.

3

If a given plane in General position, let's call them a(m,v) and b (ABC), the construction of the line between the two planes make by entering two auxiliary clipping planes (y and b). Then find the line of intersection of these planes with the planes, which are set according to the requirement of the job. Let y plane will intersect with plane a in a straight line (12), and plane b along a straight line (34). Direct (12) and (34) have a common intersection point P, which simultaneously belongs to the three planes a, b and y. Suppose that a plane intersects the plane a along a straight line (56) and plane b along a straight line (78). The point of intersection of lines (56) and (78) (she belongs to three planes a, b and y, as well as lines of intersection of the planes a and b). In view of this, RC will be the line of intersection of the planes a and b.

Note

Not to get confused with the name of the planes!

Useful advice

There are the following schemes of constructing the line of intersection of surfaces: cross-sections of the sphere and the clipping plane.