section_path: Dot product and generalisations
section_name: Dot product and generalisations
paragraph_text: Dot product and generalisations
  
  In the Euclidean space, the angle θ between two Euclidean vectors u and v is related to their dot product and their lengths by the formula
  
  u ⋅ v = cos (θ) ‖ u ‖ ‖ v ‖. {\displaystyle \mathbf {u} \cdot \mathbf {v} =\cos(\theta)\left\|\mathbf {u} \right\|\left\|\mathbf {v} \right\|.}
  
  This formula supplies an easy method to find the angle between two planes (or curved surfaces) from their normal vectors and between skew lines from their vector equations.