Home/Algebra/Orthogonality and projections/Orthogonality21. Orthogonality and projectionsOrthogonalityLevel: intermedioIn 21. Orthogonality and projectionsFormulaCopy LaTeXu⊥v ⟺ u⋅v=0u\perp v\iff u\cdot v=0u⊥v⟺u⋅v=0Tagsalgebraalgebra formulalinearorthogonalityorthogonality projectionsDetailCharacterizes perpendicular vectors.Explore the ideaFound an error? Contact us.Related formulasRelatedDot productu⋅v=∑iuivi=∥u∥∥v∥cosθ\mathbf u\cdot\mathbf v=\sum_i u_iv_i=\|u\|\|v\|\cos\thetau⋅v=i∑uivi=∥u∥∥v∥cosθOpen formulaOpen in sectionRelatedOrthogonal projectionprojb(a)=a⋅b∥b∥2b\operatorname{proj}_b(a)=\frac{a\cdot b}{\|b\|^2}bprojb(a)=∥b∥2a⋅bbOpen formulaOpen in section