# Vector Proof Homework: The Rotation Matrix

• Andrew11
In summary, a rotation matrix is a 3x3 square matrix used to rotate vectors or objects in 3D space. It is represented by sine and cosine functions and is denoted by the symbol R. Its purpose is to transform objects without changing their length or direction and it is commonly used in computer graphics, physics, and engineering. To perform vector proof homework using a rotation matrix, one must identify the given vector and axis of rotation, use the rotation matrix formula, and use the new coordinates to prove the correct rotation. Additionally, a rotation matrix can also be used for 2D transformations with similar principles and formulas.
Andrew11

## Homework Equations

The Rotation Matrix

## The Attempt at a Solution

I am sorry but I do not know how to even begin

Hello Andrew, (welcome back, that is.)

Not much joy with thread #1, I see. You should know that PF guidelines don't allow help unless an attempt at solution is posted. Least you could do is write down a rotation matrix as described in the problem statement and let it loose on the vector.

## 1. What is a rotation matrix?

A rotation matrix is a mathematical tool used to rotate a vector or an object in 3D space. It is a square matrix with dimensions 3x3 and is used to perform rotations around a specific axis.

## 2. How is a rotation matrix represented?

A rotation matrix is represented by a combination of sine and cosine functions, which describe how the vector or object is rotated around an axis. It is usually denoted by the symbol R.

## 3. What is the purpose of using a rotation matrix?

The purpose of using a rotation matrix is to transform a vector or an object in 3D space without changing its length or direction. It is commonly used in computer graphics, physics, and engineering applications.

## 4. How do you perform vector proof homework using a rotation matrix?

To perform vector proof homework using a rotation matrix, you need to follow a series of steps. First, identify the given vector and the axis of rotation. Then, use the rotation matrix formula to calculate the new coordinates of the vector after rotation. Finally, use the new coordinates to prove that the vector has been rotated correctly.

## 5. Can a rotation matrix be used for 2D transformations as well?

Yes, a rotation matrix can also be used for 2D transformations. In 2D space, the rotation matrix is a 2x2 matrix and is used to rotate vectors or objects around a point on the coordinate plane. The principles and formulas used are similar to those used in 3D space.

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