Question

Is cross product distributive over dot product?

Answer 1

Determine if the cross product is distributive over dot product

Cross product is the product of the magnitude of the vectors and the sine of the angle between them.

While dot product is the product of the magnitude of the vectors and the cosine of the angle between them.

Cross product, also known as vector product, is distributive across the addition of vectors such that:

$a\times (b+c)=a\times b+a\times c$

Similarly, dot product or scalar product is also distributive over vector addition.

$a.(b+c)=a.b+a.c$

Therefore, we can say that the cross product is distributive over dot product.