# Dot Product Calculator

> Calculate the dot product, vector magnitudes, and angle between two numeric vectors.

Page: https://askcalculators.com/calculator/dot-product-calculator/
Definition: https://askcalculators.com/calculator/dot-product-calculator/definition.json
JSON Schema: https://askcalculators.com/calculator/dot-product-calculator/schema.json
Version: 1.0.0
Maintained by: AskCalculators (software project; not a credentialed reviewer)
Qualified review: pending. Automated checks do not establish professional approval.
Page status: Live
Review status: Pending

## Use
Open the calculator page and enter values. Query-string parameters can restore and bookmark a calculation.
Example: https://askcalculators.com/calculator/dot-product-calculator/?vectorA=1%2C+2%2C+3&vectorB=4%2C+-5%2C+6

## Inputs
- vectorA: Vector A; type=text; required; default=1, 2, 3
- vectorB: Vector B; type=text; required; default=4, -5, 6

## Outputs
- dotProduct: Dot product; format=number; primary
- magnitudeA: |A|; format=number
- magnitudeB: |B|; format=number
- angleDegrees: Angle between vectors; format=number
- orthogonality: Relationship; format=text

## Formula
A · B = Σaᵢbᵢ; cos θ = (A · B) ÷ (|A||B|)

## Rules
- Empty optional inputs are undefined, not zero.
- Hidden conditional inputs are ignored.
- Do not invent missing required inputs.