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
Step 1: Gather your data values
- 2
Step 2: Apply the formula
- 3
Step 3: Perform the calculations
- 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