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You will need

• - a simple pencil;
• - notebook;
• - a pen.

Instructions

1

Carefully study the conditions of the task: from how correctly you understand it, the final result depends to a large extent.

2

To construct the intersection line of two planesfind two common points of these planes, through which in the future you will draw a straight line. Note that the plane specified by the triangle ABC can be represented by straight lines (AB), (AC), (BC). The point at which the line (AB) intersects the plane a ", denote D, and call the line (AC) the point F. Thus, the segment (DF) will determine the line of intersection of these two planes .Because a is a horizontally projecting plane , the projection of the segment D1F1 will coincide with the trace from the plane a1 1. It follows that you only need to construct the missing projections of the segment (DF) on the planes P2, and also P3.

3

In the case when given a plane of generalposition, call them a (m, v) and b (ABC), draw a line between two planes by entering two auxiliary intersecting planes (y and c). After that, find the intersection lines of these planes with those planes that are given by the job condition. Let the plane y intersect the plane a along the line (12), and with the plane b - along the line (34). The lines (12) and (34) have a common point of intersection P, which simultaneously belongs to the three planes a, b and y. Suppose that the plane в intersects with the plane a along the line (56), and with the plane b - along the line (78). The point of intersection of lines (56) and (78) - K (it belongs to three planes a, b and y, and also intersection lines of planes a and b). In view of this, the RC is the line of intersection of the planes a and b.

Tip 2: How to determine the intersection line of planes

In space, two planes can be parallel, coinciding and intersecting. Line intersections two planes This is a straight line, for the construction of which it is necessary to determine two points common to these planes.

You will need

• - ruler;
• - a pen;
• - A simple pencil.

Instructions

1

Construct two non-parallel planes, which at the same time should not coincide with each other, and name them a and b

2

Let the plane b be given by a triangle (ABC). To solve this problem, you need to find two points that are simultaneously common to two planes, and draw a straight line through them line.

3

The plane b can be represented by three straight lines: AB, BC and AC. Point intersections Direct AB with the plane a call the point D.

4

Find the point intersections plane a with a straight line AC and call it the point F. The segment DF will be a line suppression of two planes.

5

A particular case of intersecting planes - mutually perpendicular to the plane. Two intersecting planes will be perpendicular if the third plane (we call it g) is perpendicular to the line intersections given planes (a and b). In other words, the plane a will be perpendicular to the plane b if the plane g is perpendicular to the straight line c (being the line intersections planes a and b), while the straight line a will belong to the plane a, and the line b to the plane b.

6

The first sign of the perpendicularity of the two planes: if the plane b belongs to the straight line b, which in turn is perpendicular to the plane a, then the planes a and b are perpendicular to each other.

7

The second sign of the perpendicularity of the planes: if the plane is perpendicular to the plane andTo the plane a a perpendicular is drawn, which has a common point with the plane b, then this perpendicular lies in the plane b. A straight line passing between perpendicular planes (in this case straight line c), and will be a line intersections given planes.