Why normalize a vector

A unit vector keeps direction but fixes length at 11. That makes it useful when direction matters more than raw size.

The standard rule is hat{u}= ec{v}/lVert ec{v} Vert, so the zero vector is excluded because its length is zero.

Where it helps

  • Separating direction from magnitude in physics and geometry.
  • Building direction fields, normals, and projection formulas.
  • Standardizing vectors before angle or similarity comparisons.