Linear Algebra

Vector Magnitude & Unit Vector

Compute ‖v‖ = √(v₁² + v₂² + ...) and the unit vector vÌ‚ = v/‖v‖ for 2D and 3D vectors. Includes direction angle and verification that ‖vÌ‚‖ = 1.

Inputs
Vector v

Visualization — v (blue) vs vÌ‚ (gold) on unit circle

Step-by-Step Work

Put It Into Practice

The calculator shows the steps — a quiz proves you can do them on your own.

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