Doubt about an operation involving vectors

Question

Given $\vec{u}=(1;2;-1)$ and $\vec{a}=(1;-3;4)$, calculate $\vec{u}-\frac{3}{\vec{u}} . \vec{a}$.

Well, I think that the operation $\frac{3}{\vec{u}}$ is not defined, is it? In case it's possible, what should I do?

Answer 1

You are correct; there's no concept of dividing by a vector.

It may be a typo in the problem you're solving -- perhaps it should be $ \vec u - \frac3{\vec u\cdot \vec a}\cdot \vec a$ or $\vec u - \frac{3}{|\vec u|}\cdot\vec a $?

Or perhaps it is some idiosyncratic notation that you'll have to ask the person who gave you the problem about.

Answer 2

Nothing. You are right: it is undefined.

Perhaps that whover wrote it meant $\dfrac3{\left\lVert\vec u\right\rVert}$.

Answer 3

Perhaps $\frac1{\vec{u}} $ is a vector such that $\frac1{\vec{u}}\times\vec{u} =I $.