Linear Algebra
Dot Product - Linear Algebra
Learn the dot product with examples, step-by-step guide, and calculator tools. Scalar product of vectors
The dot product is a fundamental concept in linear algebra. Scalar product of vectors. This page provides a comprehensive guide with worked examples and practical applications.
The Formula
\[\vec{a} \cdot \vec{b} = \sum_{i=1}^{n} a_ib_i = |\vec{a}||\vec{b}|\cos\theta\]
Variables
a⃗·b⃗
Dot product
θ
Angle between vectors
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, 2, 3]·[4, 5, 6] = 1×4 + 2×5 + 3×6 = 32
Example 2
Example 2: 32
Frequently Asked Questions
What is the dot product?
Scalar product of vectors
How do I calculate dot product?
Use the formula: \vec{a} \cdot \vec{b} = \sum_{i=1}^{n} a_ib_i = |\vec{a}||\vec{b}|\cos\theta. Follow the steps provided above.
What tools can help with dot product?
We provide online calculators: calculator