Remember the following formula for the scalar multiplication of a number times a vector.
Let v be a vector such that v = (a,b), and let k be a real number. Then:
[tex]k\vec{v}=k(a,b)=(ka,kb)[/tex]If u=(1,-3), then:
[tex]\begin{gathered} \frac{1}{3}\vec{u}=\frac{1}{3}(1,-3) \\ =(\frac{1}{3}\times1,\frac{1}{3}\times-3) \\ =(\frac{1}{3},-1) \end{gathered}[/tex]Therefore, the answer is option B:
[tex](\frac{1}{3},-1)[/tex]