Vector Dot Product
GeometryEasyCompute scalar projections and angles between vectors.
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Dot Product Vector Grid (Drag Origin A, U head, or V head)
Vector U:[5, 0]
Vector V:[3, 4]
Dot Product value:15
Angle Between (θ):53.13°
Time Complexity
O(1) direct equation
Space Complexity
O(1) auxiliary
Conceptual Overview
The Vector Dot Product U · V computes the projection scaling of V onto U. It is key for checking orthogonality and calculating segment angles.
Mathematical Formula
U \cdot V = U.x \cdot V.x + U.y \cdot V.y = |U||V|\cos(\theta)
Source: CP-Algorithms geometry reference