Three Dimensional Geometry

In this topic, we will determine the direction cosines and direction ratios of a line. We will also learn the relation between direction cosines, direction cosines of line joining two points, and the angle between two lines.

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.

From this topic, we will learn how to determine the equation of a straight line in three dimensional geometry. We will study the parametric and symmetric form of a line. It also includes the equation of the straight line through two given vectors.

The topic focuses on the vector form of the equation of the lines. It includes the two different vector forms of the equation of line when the two given non-parallel lines intersect. Furthermore, question banks are given for practice.

In this topic, we will learn about the representation of points and lines in three dimensional geometry. We will also talk about the direction cosines of a line. Moreover, we will discuss the condition of perpendicularity of lines.

In this topic, we will read about two intersecting lines in three dimensional geometry. We will also learn how to find the point of intersection of two lines. It also covers some examples to teach us in a better way.

In this topic, the equation of the plane is discussed with the help of the figure. It mentions the cartesian equation of the plane known as normal form of the equation along with the two corollaries that include the standard and general form.

The topic includes various forms of the equation of the plane. We will study the vector form, cartesian form that includes the one point form, standard form and the general form of the cartesian equation with the illustrative examples.

This topic helps us to determine the image of a point about the plane and the foot of a perpendicular with the help of illustrative examples. The concept of direction ratios is also used in the topic. In addition, exercise is given for the practice.

In this topic, we will learn to find the vector equation of the plane. We will study to find the vector equation of a plane perpendicular to a given direction and a given distance from the origin with the help of figure.

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 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.

In this topic, we will learn the different types of planes that are specified in various ways. It briefs the family of planes, various forms of the equation of plane and the examples based on it.

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.