Find the cross product of two 3D vectors with magnitude and direction.
The cross product A × B of two 3D vectors produces a vector perpendicular to both A and B. Its magnitude equals the area of the parallelogram spanned by A and B. The direction follows the right-hand rule. The cross product is only defined in 3 dimensions (and 7 dimensions).
Cross Product
A × B = [A₂B₃−A₃B₂, A₃B₁−A₁B₃, A₁B₂−A₂B₁]
Magnitude
||A × B|| = ||A|| · ||B|| · sin(θ)
No. A × B = −(B × A). The cross product is anti-commutative — swapping the operands reverses the direction.
When the vectors are parallel (or one is the zero vector). Parallel vectors span no area, so the cross product magnitude is zero.