Question

Why does multiplication of vectors not have a corresponding division?

Answer 1

It can have...

Explanation:

The normal kinds of multiplication of vectors that you have probably encountered are dot product and cross product.

• Dot product does not support division since it makes two vectors into one scalar.

• Cross product does not support division, since the cross product of two non-zero vectors in the same direction is zero.

However, they can be combined into quaternion multiplication in four dimensional space, creating a form of multiplication that does support division by any non-zero element.

See https://socratic.org/s/aCwSAEhJ for some more details.