CPKit
v1.6.1

Vector Cross Product

GeometryEasy

Compute signed area magnitude spanned by 2D vectors.

Alt+Shift+C

Cross Product Vector Grid (Drag Origin A, U head, or V head)

Origin (A) (0, 0)Vector U (B) (4, 2)Vector V (C) (1, 4)
Vector U:[4, 2]
Vector V:[1, 4]
Cross Product magnitude (signed area):14

Time Complexity

O(1) direct equation

Space Complexity

O(1) auxiliary
Conceptual Overview

The 2D Vector Cross Product (or skew product) U × V computes the signed area of the parallelogram spanned by the two vectors.

Mathematical Formula
U \times V = U.x \cdot V.y - U.y \cdot V.x = |U||V|\sin(\theta)
Source: CP-Algorithms geometry reference