Coordinate System In 3d Space

The coordinate system in 3D space allows us to represent points in a three-dimensional environment using coordinates (x, y, z).

The Cartesian Coordinate System

The Cartesian coordinate system enables representation of points in a 3D space using three coordinates (x, y, z).

Plotting A Point In 3d

This section explains how to plot points in three-dimensional space using Cartesian coordinates.

Distance Between Two Points In Space

This section covers the method for calculating the distance between two points in three-dimensional space using the 3D version of the Pythagorean theorem.

Section Formula In 3d

The Section Formula in 3D defines how to determine a point that divides a line segment in space based on given ratios.

Midpoint Of A Line Segment In 3d

The midpoint of a line segment in 3D space is calculated by averaging the coordinates of the endpoints, providing important insights into spatial relationships.

Equation Of A Line In 3d

This section covers the various ways to represent a line in three-dimensional space, focusing on the parametric and symmetric forms of the line equation.

Parametric Form

The parametric form is a way to represent a line in 3D space using a point and a directional vector.

Symmetric Form

The symmetric form of a line in three-dimensional space provides a compact way to represent a line using ratios of the differences in coordinates.

Equation Of A Plane

The Equation of a Plane section introduces and explains the mathematical concepts and forms used to represent planes in three-dimensional space.

General Form

This section introduces the general equation of a plane in three-dimensional space, focusing on its structure and components.

Plane Passing Through A Point

This section introduces how to formulate the equation of a plane passing through a specific point in 3D space with a defined normal vector.

Angle Between Two Planes

The angle between two planes is determined by the orientation of their normal vectors and is calculated using the dot product of the normals.

Distance From A Point To A Plane

This section discusses how to calculate the distance from a point to a plane in three-dimensional space.

Sphere

A sphere is defined as the set of all points in space equidistant from a center point.

Definition

A sphere is defined as the set of all points in space at a fixed distance from a central point, known as the center.

Equation Of A Sphere

The equation of a sphere describes the geometric relationship of all points equidistant from a central point in three-dimensional space.

Right Circular Cylinder And Cone

This section covers the concepts and equations of right circular cylinders and cones, including their definitions and mathematical representations.

Cylinder

A right circular cylinder is formed when a line segment moves parallel to itself along an axis, and its equation varies based on the orientation of its axis.

Cone

This section introduces the concept of a right circular cone, detailing its properties and the equation used to represent it in three-dimensional geometry.

Problems And Examples

This section presents practical examples and problems related to the concepts of 3D geometry, including distance calculations and equations of planes.