∠︎

Computes the angle between two vectors.

Syntax

• ∠(u, v)

  • u and v are vectors

Description

If u and v are vectors of the same dimension, then ∠(u, v) is the angle between them.

For real vectors,

∠(u, v) = arccos((u | v) / [norm(u)⋅norm(v)])

For complex vectors,

∠(u, v) = arccos(Re(u | v) / [norm(u)⋅norm(v)]).

Notes

∠ is a synonym of angle.

Examples

∠(❨2, 1, 0, 2❩, ❨−1, 2, 1, 0❩)

1.57079632679	(=π/2)

See also

• angle

• ⋅ (|, InnerProduct)

• ⟂ (ArePerpendicular)

• ∥ (AreParallel)

• ∦ (AreNotParallel)