Answer:
[tex]||v||=\frac{1}{3}\sqrt{37}[/tex]
Explanation:
Given a vector v=, its magnitude is calculated using the formula:
[tex]||\vec{v}||=\sqrt{x^2+y^2}[/tex]
Therefore for the vector <1/3, -2>:
[tex]\begin{gathered} ||v||=\sqrt{\left(\frac{1}{3}\right)^2+\left(-2\right)^2} \\ =\sqrt{\frac{1}{9}+4} \\ =\sqrt{\frac{37}{9}} \\ =\frac{\sqrt{37}}{3} \\ ||v||=\frac{1}{3}\sqrt{37} \end{gathered}[/tex]
The magnitude of the vector is 1/3√37.
The first option is correct.
