Three Dimensional Geometry

This topic defines the direction cosines and direction ratios of a line. It also explains the formulas applied to them through examples and exercises.

In this topic, we will discuss theorems related to equations of a line in space. The algorithm related to equations of a line is discussed here in detail along with illustrative examples and exercises.

In this topic, we will learn to find the angle between two lines, either in vector form or Cartesian form. Conditions for perpendicularity and parallelism for both vectors and the Cartesian system are also elucidated here.

In this topic, we will learn to find the shortest distance between two straight lines. The shortest distance between skew lines in vector and Cartesian form and the line of shortest distance is explained here through figures.

In this topic, we will learn the basic definition of the plane. Theorems related to the plane are also discussed here through illustrated examples and exercises.

This topic discusses the coplanarity of two lines with the help of examples. It explains the criteria of coplanarity of lines, along with the required conditions for it.

In this topic, we will learn to find the angle between two planes. Conditions of perpendicularity and parallelism in Cartesian form and vector form are also given here.

In this topic, we will learn to find the perpendicular distance of a point from a plane in both Cartesian and vector form. Theorems related to vector form and Cartesian forms are also explained here in detail.

In this topic, we will discuss the unsymmetrical form of a line. The reduction of unsymmetrical form to symmetrical form and intersection of a line and a plane are also explained here.