Table of Contents

**Introduction To 3D Geometry**

A three-dimensional geometry is a branch of mathematics that studies the properties of shapes in three dimensions. It is an extension of two-dimensional geometry, which studies shapes in two dimensions. Just as in two dimensions, shapes in three dimensions can be classified according to their properties.

There are three basic types of shapes in three dimensions: points, lines, and planes. Points are the simplest shapes, and they have no dimensions. Lines are one-dimensional shapes, and they are defined

## Introduction to 3-Dimensional Geometry

3-dimensional geometry is the study of shapes in three dimensions. These shapes can be points, lines, planes, and solids. In 3-dimensional geometry, we use three coordinates to describe the location of a point in space. The three coordinates are x, y, and z.

The most basic shapes in 3-dimensional geometry are points, lines, and planes. A point is a location in space with no dimensions. A line is a location in space with one dimension

### Coordinate System in 3D Geometry

A coordinate system is a way of representing points in space using numbers. In a three-dimensional coordinate system, points are represented by three numbers, called coordinates. The first coordinate is the distance from the origin in the x-direction. The second coordinate is the distance from the origin in the y-direction. The third coordinate is the distance from the origin in the z-direction. The origin is the point at (0,0,0).

Here is an example of a

### The Properties of Three-dimensional Space:

In mathematics, three-dimensional space is a geometric setting with three dimensions. It is the natural setting for most physical objects and phenomena. All the objects we experience in our everyday lives exist in three-dimensional space. This space is commonly represented in mathematical models by three coordinate axes (x, y, and z) that intersect at the origin. Points in three-dimensional space are usually described by a triplet of real numbers, (x, y, z).

#### Rectangular Coordinate System in Space

A rectangular coordinate system is a coordinate system that uses perpendicular lines called axes to identify points in a plane or in space. The axes are usually labeled x and y, or east-west and north-south. The point where the axes intersect is called the origin.

Points in a plane can be identified by their distance from the origin and their direction. Points in space can be identified by their distance from the origin, their direction, and their altitude.

The coordinate system can

#### Coordinates of a Point in Space

A point in space can be located by its coordinates. A coordinate is a number that uniquely identifies a point in space. The coordinate system is based on a set of axes that are perpendicular to each other. The x-axis is horizontal and the y-axis is vertical. The z-axis is perpendicular to the x- and y-axes and extends out of the page.

The coordinate of a point can be written as (x, y, z). The x-

**Some Key Points to Remember**

About the Holocaust

Some key points to remember about the Holocaust are:

1. The Holocaust was a genocide in which Nazi Germany killed six million Jews.

2. The Holocaust was the result of a long and systematic process of demonization of the Jews by the Nazis.

3. The Nazis used a variety of means to kill the Jews, including mass shootings, gas chambers, and concentration camps.

4. The Holocaust was one of the worst atrocities in human history

**Direction Cosines of a Line**

In mathematics, direction cosines are used to represent the direction of a vector in three-dimensional space. A vector is represented as an arrow with a certain length and a certain direction. The direction of the vector is given by its direction cosines.

There are three direction cosines, one for each dimension. The direction cosine for the x-axis is the cosine of the angle between the vector and the x-axis. The direction cosine for the y-axis

#### Perpendicular Distance of a Point from a Line

A point is said to be perpendicular to a line if it is at a right angle to the line. The distance of a point from a line is the length of the line segment from the point to the line. The perpendicular distance of a point from a line is the length of the line segment from the point to the line at a right angle to the line.

### Difference between 2D Shape and 3D Geometric Shape

A 2D geometric shape is a shape that has two dimensions- width and length. A 3D geometric shape is a shape that has three dimensions- width, length, and height.

2D shapes can be flat or curved. 3D shapes can be curved, but they can also be solid, like a ball or a cube.

2D shapes can be drawn on a piece of paper. 3D shapes can be made out of materials like wood, metal,

**Also Read: 3d Geometry- properties, Coordinate system.**