EQUATIONS OF A PLANE AND A STRAIGHT LINE IN SPACE

Abstract

This work studies the analytical representation of plane and straight line equations in space, their types, geometric interpretation, and mutual localization cases. In a three-dimensional coordinate system in space, general, point-vector, and normal equations of the plane are introduced. Also, parametric and direction vector equations of a straight line are covered. During the work, the relationship between a plane and a straight line, the conditions for their intersection, and the cases of parallelism and perpendicularity are analyzed. Also, attention is paid to important geometric concepts such as the distance from a point to a plane or straight line, angle, and projection.

This topic occupies an important place in the analytical geometry section of mathematics and is widely used in the fields of engineering, physics, and computer graphics. As a result of the work, students will acquire the skills to represent and analyze the main geometric objects in space in an analytical form.