---
tag: DR32G8ZZNM
kind: concept
name: Vector algebra relations
aliases: [quadruple-product, scalar-quadruple-product, vector-algebra-identities, vector-quadruple-product]
sources:
  - wikipedia: en:28810270@r1374428197
    locator: Vector algebra relations
    note: adopted
    mention: wikipedia://en/28810270
    sections: [Summary]
same_as:
  wikidata: Q7917817
  wikipedia: Vector algebra relations
inventory: [EA8RGE66DQ]
---

## Summary

The following are important identities in [[vector algebra|000AYPA9AJ]]. Identities that only involve the magnitude of a vector $\|\mathbf A\|$ and the [[dot product|0S52TNNTH9]] (scalar product) of two vectors **A**·**B**, apply to vectors in any dimension, while identities that use the [[cross product|0N5N15HWZ7]] (vector product) **A**×**B** only apply in three dimensions, since the cross product is only defined there. Most of these relations can be dated to founder of vector calculus Josiah Willard Gibbs, if not earlier.