Linear Algebra
Class 12

Vector Cross Product

a×b=absinθn^\vec{a} \times \vec{b} = |\vec{a}||\vec{b}|\sin\theta \hat{n}
00.511.522.530510152025
a × b = |a||b|sin(θ) n̂

Adjust Variables

Vector magnitude
mag =
110

Vector product gives perpendicular vector. Magnitude equals parallelogram area. Direction by right-hand rule.

Real-World Applications

Physics — Torque: τ = r × F.

Physics — Magnetic force: F = qv × B.

Physics — Angular momentum: L = r × p.

Computer graphics — Surface normal calculation for lighting.

3D modeling — Determining face orientations.

Robotics — Rotation axis calculations.

Navigation — Course correction in 3D.

Engineering — Moment calculations.

Gaming — Determining "inside" vs "outside" of polygons.

Fluid dynamics — Vorticity calculations.

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