If I have a vector 5$\vec{u}$, what should be the expression for its unit vector?
Should it be:
5$\vec{u}\frac{1}{5||\vec{u}||}$ ? OR
$\vec{u}\frac{5}{||\vec{u}||}$
And why?
I understand that that for a vector $\vec{u}$, its unit vector expression would be $\vec{u}\frac{1}{||\vec{u}||}$
In general, the unit vector in the direction of any vector $\vec{v}\neq\vec{0}$ is just $\vec{v}/||\vec{v}||$, since this vector obviously has the same direction (being multiplied by only a positive scalar factor), and also has unit length. Therefore as suggested in the comments, the unit vector in the direction of $5\vec{u}$ will be simply $$\frac{5\vec{u}}{||5\vec{u}||},$$ which is your first option. Note also that since $5\vec{u}$ is obviously in the same direction as $\vec{u}$, the unit vector must remain the same, so this gives us another way to see that the answer must be equivalent to $\vec{u}/||u||$, which is satisfied by the first option, since the scalar factor of $5$ in the numerator and denominator cancel.