Question

Is the cross-product distributive?

Answer 1

Cross-product:

If $\mathit{a}\mathrm{and}\mathit{b}$are two independent vectors, then the result of the cross-product of these two vectors $\left(a\times b\right)$ is perpendicular to both vectors and normal to the plane that contains both vectors.

1. The vector cross product is distributive over addition and is also known as the vector product.
2. If $\mathit{A}\mathbf{,}\mathbf{}\mathit{B}\mathbf{,}\mathrm{and}\mathit{C}$are three vectors, then their vector product is $A\times (B+C)=(A\times B)+(A\times C)$

Therefore, the cross-product of vectors is distributive.