A straight line in space is one of the main figures in geometry. It consists of an infinite number of abstract objects that lack volume, area, length and any other characteristics. These zero-dimensional objects also serve as fundamental figures in geometry and are called points.
A straight line in space is similar to that drawn on an existing plane. With the help of imagination, two points must be marked. Between them, as well as beyond them to infinity, a line is drawn using a ruler. This is the straight line in space. On this line you can mark a line or a point. These actions are similar to those performed on the plane.
In geometry, there are axioms that relate to the definition of a line. These include the following statements:
1. Only two single lines can be drawn through the two marked points.
2. There are cases when two separately taken points of the line are in a certain plane. Then we can say that all the zero-dimensional objects of the line are in it.
Thanks to these axioms, the assertion that the line in space lies entirely in a certain plane becomes obvious.
In geometry, another case is considered. It arises in those situations when a straight line in space appears as a result of the intersection of two different planes. The statement is true: if two different planes have at least one common point, then they have a common line. All common zero-dimensional objects of these geometric figures lie on this line .
The mutual arrangement of straight lines in space can have various options. In individual cases, they may coincide. That is, in this embodiment, the lines have an infinite number of common points.
Lines in space can have one common point. In this embodiment, these lines are in a certain plane located in three-dimensional space. This case leads to an understanding of the angle that arises between the lines.
Straight lines can be located in space in parallel. In this situation, they are on the same plane and do not intersect throughout their length.
On a straight line, as well as on a line parallel to it, a nonzero vector will be its guide. This geometric concept is often used in solving various problems. Using the vector, you can determine the direction of the line.
Lines can also be crossed. In this case, they are located in different planes. This arrangement leads to the geometric concept of the angle, which is located between the intersecting lines. Of particular interest are cases of perpendicular arrangement of lines in three-dimensional space. In such embodiments, the angle between them is a value equal to ninety degrees.
You can set a straight line in space using various methods. To perform these actions, knowledge of axioms will help. Based on the fact that only one straight line can pass through two points marked in space, we can display it by drawing a line through the outlined zero-dimensional objects.
If it is necessary to build a geometric figure in a coordinate system of a rectangular type, which is located in three-dimensional space, then an equation is drawn up. When defining a line, it is necessary to rely on the coordinates of its two points, which should be known.
In constructing the necessary line, one can use the parallelism theorem. In this case, through a certain point that does not belong to our line, we can always construct a geometric figure, all zero-dimensional objects of which will belong only to it.
A plane and a straight line in space can also be perpendicular. In this case, a geometric figure is drawn to build a line. In this case, the intersection angle of such a straight line and a plane is 90 degrees.