Cross Product Calculator - Multi-Tools

Cross Product Calculator

Vector A

x:

y:

z:

Vector B

x:

y:

z:

About Cross Product

The cross product (also called vector product) is a binary operation on two vectors in three-dimensional space. It results in a vector that is perpendicular to both input vectors.

Key Concepts:

Cross Product: A × B = (a₂b₃ - a₃b₂, a₃b₁ - a₁b₃, a₁b₂ - a₂b₁)
Magnitude: |A × B| = |A| |B| sin(θ)
Direction: Perpendicular to both input vectors
Right-hand Rule: Determines the direction of the result

Properties of Cross Product:

Anti-commutative: A × B = -(B × A)
Distributive: A × (B + C) = A × B + A × C
Scalar multiplication: (kA) × B = k(A × B)
Zero vector if vectors are parallel

Applications:

Calculating torque in physics
Finding normal vectors in computer graphics
Determining angular momentum
Solving geometric problems in 3D space

Tips:

Input vectors must be 3D
Result is perpendicular to both input vectors
Use right-hand rule to determine direction
Magnitude equals area of parallelogram formed by vectors

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