Home/Algebra/Vectors/Dot product15. VectorsDot productLevel: intermedioIn 15. VectorsFormulaCopy LaTeXu⋅v=∑iuivi=∥u∥∥v∥cosθ\mathbf u\cdot\mathbf v=\sum_i u_iv_i=\|u\|\|v\|\cos\thetau⋅v=i∑uivi=∥u∥∥v∥cosθTagsalgebraalgebra formulalinearvectorsvectors algebraDetailMeasures alignment and allows defining angles and orthogonality.Explore the ideaFound an error? Contact us.Related formulasRelatedAngle between vectorscosθ=u⋅v∥u∥∥v∥\cos\theta=\frac{u\cdot v}{\|u\|\|v\|}cosθ=∥u∥∥v∥u⋅vOpen formulaOpen in sectionRelatedOrthogonalityu⊥v ⟺ u⋅v=0u\perp v\iff u\cdot v=0u⊥v⟺u⋅v=0Open 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