Vector magnitude (or norm) measures a vector's length: |v| = √(v₁² + v₂² + ... + vₙ²). For 2D: |v| = √(x² + y²). For 3D: |v| = √(x² + y² + z²). The unit vector v̂ = v/|v| has magnitude 1 and points in the same direction.
How to Use
Enter vector components:
- Components: x, y, z (or more)
- Magnitude: √(sum of squares)
- Unit vector: Each component / magnitude
Formula
- |v| = √(Σvᵢ²)
- Unit: v̂ = v / |v|
- Direction cosines: cos(α) = vₓ/|v|
Applications
- Physics: force magnitude, velocity speed
- Graphics: normalizing vectors for lighting
- ML: feature scaling, distance metrics
Step-by-Step Instructions
- 1Enter vector components.
- 2View the magnitude.
- 3Check the unit vector.
- 4Review direction angles.
- 5Compare component contributions.