sentences:  For a (positive) Euclidean -subspace its orthogonal complement is a -dimensional negative "Euclidean" subspace, and vice versa.Generally, for a -dimensional subspace consisting of positive and negative dimensions (see Sylvester's law of inertia for clarification), its orthogonal "complement" has positive and negative dimensions, while the rest ones are degenerate and form the intersection.The parallelogram law takes the form
  
  Using the square of the sum identity, for an arbitrary triangle one can express the scalar square of the third side from scalar squares of two sides and their bilinear form product