Vector Questions

Question

So I have two questions, first of all, would a value of one divided by a magnitude of $v$ multiplied by the vector $w$ be simply an example of scalar multiplication or would it be undefined? Same goes for one divided by a vector multiplied by a magnitude. My guess is that you cannot have one divided by a vector in the first place so I believe it’s undefined am I correct?

Answer 1

• A value of one divided by a magnitude of $v$ multiplied by the vector $w$ means

$$\frac1{\|v\|}w.$$

It is well defined as long as $v \ne 0$. Note that $\frac1{\|v\|}$ is a scalar here.

• One divided by a vector is not defined.