|B| . Vector projection of A on B Given by proj B (A) = (A · B | Home › Math & Conversions › Core Math & Algebra › Vector Vector Calculator Compute magnitude, dot and cross products, angle between vectors, and projections in 2D or 3D, with formulas and geometric interpretation. Core Math & Algebra Interactive vector operations (2D & 3D) Use this tool to explore vector algebra: magnitudes, dot product, angle between vectors, sum and difference, projection of one vector onto another, and (in 3D) the cross product and its magnitude (area). 2D vectors (x, y) 3D vectors (x, y, z) Vector A A x A y A z Empty fields are treated as 0. For 2D vectors, z is implicitly 0. Vector B B x B y B z You can model 2D vectors in 3D by setting z = 0. Compute vector operations Clear Load example Vector results summary – Dimension Vector A Vector B Magnitude |A| Magnitude |B| Dot product A · B Angle θ (degrees) Angle θ (radians) |A × B| (3D) Sum A + B Difference A − B Scalar projection of A on B Component of A along the direction of B: comp B (A) = (A · B)