Instruction

1

Video is one of the fundamental geometric concepts along with the point and the plane. It's an endless shape, which you can connect any two points in space. Video always belongs to any plane. Based on the location of two straight lines, one should use different methods of finding distance between them.

2

There are three options for the location of two straight lines in space relative to each other: they are parallel, intersect or cross each other. The second option is possible only if they lie in the same plane, the first does not exclude facilities two parallel planes. The third situation suggests that direct lie in different parallel planes.

3

To find the distance between two parallel lines, it is necessary to determine the length of the perpendicular segment connecting any two points. Since direct have two identical coordinates, which follows from the definition of their parallelism, the line equation in two-dimensional coordinate space can be written as:

L1: a•x + b•y + C = 0;

L2: a•x + b•y + d = 0.

If you can find a segment length using the formula:

s = |s - d|/√(a2 + b2), and it is easy to see that if C = D, i.e., direct matching, the distance will be zero.

L1: a•x + b•y + C = 0;

L2: a•x + b•y + d = 0.

If you can find a segment length using the formula:

s = |s - d|/√(a2 + b2), and it is easy to see that if C = D, i.e., direct matching, the distance will be zero.

4

It is clear that the distance between intersecting straight lines in two-dimensional coordinate system has no meaning. But when they are located in different planes, it is possible to find the length of a line lying in a plane perpendicular to both of them. The ends of this segment will be the point being the projection of any two points direct to the surface. In other words, its length equal to the distance between parallel planes containing these lines. Thus, if the plane is set to the General equations:

α: A1•x + B1•y + C1•z + E = 0,

β: A2•x + B2•y + C2•z + F = 0,

distance between lines can be calculated by the formula:

s = |E – F|/√(|A1•A2| + B1•B2 + C1•C2).

α: A1•x + B1•y + C1•z + E = 0,

β: A2•x + B2•y + C2•z + F = 0,

distance between lines can be calculated by the formula:

s = |E – F|/√(|A1•A2| + B1•B2 + C1•C2).

Note

In General, direct and skew in particular is interesting not only for mathematicians. Their properties are useful in many other applications: in building and architecture, in medicine and in nature.