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Vector Calculator

Perform vector operations with detailed step-by-step solutions!

Vector Calculator
Compute Vector Operations:

Try the following examples:

[Dot Product Example] [Cross Product Example] [Magnitude Example] [Addition Example] [Subtraction Example] [Angle Example]
First Vector:
Second Vector:
Optional for operations like magnitude.
Operation:

Embed Vector Calculator Widget

About Vector Calculator

Welcome to our Vector Calculator, a powerful tool designed to perform vector operations with detailed step-by-step solutions and visualizations. This calculator is ideal for students, teachers, and anyone working with vector algebra and vector calculus.

Features of the Vector Calculator

Understanding Vector Operations

Vectors are mathematical objects with both magnitude and direction. They are fundamental in physics and engineering.

Dot Product

The dot product of two vectors \( \mathbf{A} \) and \( \mathbf{B} \) is given by:

\[ \mathbf{A} \cdot \mathbf{B} = \sum_{i=1}^{n} A_i B_i \]

It results in a scalar and measures the magnitude of one vector in the direction of another.

Cross Product

The cross product of two vectors in three-dimensional space is given by:

\[ \mathbf{A} \times \mathbf{B} = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ A_x & A_y & A_z \\ B_x & B_y & B_z \\ \end{vmatrix} \]

It results in a vector that is perpendicular to both \( \mathbf{A} \) and \( \mathbf{B} \).

Magnitude

The magnitude of a vector \( \mathbf{A} \) is given by:

\[ ||\mathbf{A}|| = \sqrt{A_x^2 + A_y^2 + A_z^2} \]

It represents the length of the vector.

Angle Between Vectors

The angle \( \theta \) between two vectors \( \mathbf{A} \) and \( \mathbf{B} \) is given by:

\[ \cos(\theta) = \frac{\mathbf{A} \cdot \mathbf{B}}{||\mathbf{A}|| \times ||\mathbf{B}||} \]

This formula helps in finding the directionality between vectors.

How to Use the Vector Calculator

Applications of the Vector Calculator

Our vector calculator is especially useful for:

Why Use Our Vector Calculator?

Calculating vector operations manually can be tedious. Our calculator simplifies the process by providing:

Additional Resources

For more information on vector operations and their applications, check out the following resources:

Reference this content, page, or tool as:

"Vector Calculator" at https://MiniWebtool.com/vector-calculator/ from MiniWebtool, https://MiniWebtool.com/

by miniwebtool team. Updated: Nov 21, 2024

You can also try our AI Math Solver GPT to solve your math problems through natural language question and answer.

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