gen-in-3-4-sentences-explain-the-cross-product-state-any-key-for-e4e9

In 3-4 sentences, explain the cross product. State any key formula.

The cross product is an operation between two vectors in 3D space that produces a third vector perpendicular to both original vectors. The magnitude of the resulting vector equals the area of the parallelogram formed by the two input vectors and is given by |**a** × **b**| = |**a**||**b**|sin(θ), where θ is the angle between them. The cross product is calculated using the formula **a** × **b** = (a₂b₃ - a₃b₂)**i** + (a₃b₁ - a₁b₃)**j** + (a₁b₂ - a₂b₁)**k**, where **a** = (a₁, a₂, a₃) and **b** = (b₁, b₂, b₃). Unlike the dot product, the cross product is not commutative; instead, **a** × **b** = -(**b** × **a**).