Linear Algebra
Advanced

Cross Product Magnitude

Magnitude of the vector perpendicular to two vectors.

Formula

∣a⃗×b⃗∣=∣a∣∣b∣sin⁡θ|\vec{a}\times\vec{b}| = |a||b|\sin\theta

Variables

\vec{a},\vec{b}Vectors
\thetaAngle between them

Example

For perpendicular unit vectors, |a×b| = 1·1·sin90° = 1.

Did You Know?

The cross product exists cleanly only in 3-D — it gives a vector perpendicular to both inputs.

vectorcross product