Coordinate System In 3d Space

This section introduces the three-dimensional coordinate system, explaining how points are represented in 3D space using ordered triplets and how space is divided into octants.

Octants

In the 3D coordinate system, space is divided into eight octants, serving as extensions of the two-dimensional quadrants.

Distance Between Two Points

This section covers the formula and concept of calculating the distance between two points in three-dimensional space.

Section Formula In 3d

The section focuses on understanding the Section Formula in 3D geometry, highlighting how to find a point dividing a line segment in a given ratio.

Internal Division

This section explains the internal division of a line segment in 3D space using the section formula.

Midpoint Formula

The Midpoint Formula allows for the calculation of the point that is equidistant from two given points in three-dimensional space.

Direction Cosines And Direction Ratios

Direction cosines represent the angles a line makes with the coordinate axes, while direction ratios are proportional sets of values that help describe the same line in three-dimensional space.

Equation Of A Line In Space

This section introduces the equations of a line in three-dimensional space, covering vector, parametric, and symmetric forms.

Vector Form

This section introduces the vector form of the equation of a line in 3D space.

Parametric Form

The parametric form represents the equations of a line in three-dimensional space using parameters, making it easier to describe movement along the line.

Symmetric Form

The Symmetric Form of a line in three-dimensional geometry expresses the coordinates of points on the line in terms of its direction ratios.

Angle Between Two Lines

This section covers the calculation of the angle between two lines in three-dimensional space using direction ratios.

Skew Lines And Shortest Distance

This section explains the concept of skew lines and how to calculate the shortest distance between them.

Shortest Distance (D) Between Skew Lines

This section focuses on calculating the shortest distance between two skew lines using the vector representation.

Equation Of A Plane

This section discusses the general form, vector form, and normal form of the equation of a plane in three-dimensional space.

General Form

In this section, we explore the general form of the equation of a plane in three-dimensional geometry, highlighting its components and related forms.

Vector Form

Vector form provides a concise representation of lines in three-dimensional space using position and direction vectors.

Normal Form

Normal Form describes the equation of a plane in three-dimensional space, providing a systematic method to represent planes using specific coordinates.

Angle Between Two Planes

This section outlines the method to calculate the angle between two planes in a three-dimensional space using their normal vectors.

Angle Between A Line And A Plane

This section explains how to calculate the angle between a line and a plane using direction vectors and normal vectors.