Linear Algebra

Cross Product - Linear Algebra

Learn the cross product with examples, step-by-step guide, and calculator tools. Vector product perpendicular to both vectors

The cross product is a fundamental concept in linear algebra. Vector product perpendicular to both vectors. This page provides a comprehensive guide with worked examples and practical applications.

The Formula

\[\vec{a} \times \vec{b} = |\vec{a}||\vec{b}|\sin\theta \vec{n}\]

Variables

a⃗×b⃗
Cross product
n⃗
Unit normal vector

Step-by-Step Guide

  1. 1

    Step 1: Gather your data values

  2. 2

    Step 2: Apply the formula

  3. 3

    Step 3: Perform the calculations

  4. 4

    Step 4: Interpret the result

Examples

Example 1

Example 1: [] → [1, 0, 0] × [0, 1, 0] = [0, 0, 1]

Example 2

Example 2: [0, 0, 1]

Frequently Asked Questions

What is the cross product?

Vector product perpendicular to both vectors

How do I calculate cross product?

Use the formula: \vec{a} \times \vec{b} = |\vec{a}||\vec{b}|\sin\theta \vec{n}. Follow the steps provided above.

What tools can help with cross product?

We provide online calculators: calculator

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