Vector Magnitude

Vectors & Geometry · 1881

Equation: |v| = √(v_x² + v_y² + v_z²)
Field: Vectors & Geometry
Symbols: v a vector · v_x, v_y, v_z its components along three perpendicular axes · |v| its length, a plain number
Year: 1881

Significance

Pythagoras applied twice, and the first thing you do with any quantity that has a direction — velocity, force, field. Everything on this site that reads r² in a denominator, from gravitation to Coulomb's law, is this: the squared length of the vector from source to point. Written in Gibbs's notation of 1881; the geometry is 2,400 years older.

Requires

Pythagorean Theorem

Required By

Dot Product Cross Product Momentum and Impulse Centripetal Acceleration Law of Universal Gravitation Coulomb's Law Electric Field

Referenced by

equation

Centripetal Acceleration Coulomb's Law Cross Product Dot Product Electric Field Law of Universal Gravitation Momentum and Impulse Pythagorean Theorem

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From the Equations database in Notion, last edited 2026-08-18. This page is the row, rendered by the build; nothing on it is written by hand.