Answer
$a.) \ \vert \vert u \vert \vert = \dfrac{\sqrt{5}}{2}$
$b.) \ \vert \vert v \vert \vert = \dfrac{\sqrt{17}}{2}$
$c.) \ \vert\vert u+v\vert\vert =3$
Work Step by Step
Given $u =(1,\frac{1}{2})$ and $v = (2,-\frac{1}{2})$
$a.) \ \vert \vert u \vert \vert = \sqrt{(1)^2+(\frac{1}{2})^2} = \sqrt{1+\frac{1}{4}} = \sqrt{\frac{5}{4}} = \dfrac{\sqrt{5}}{2}$
$b.) \ \vert \vert v \vert \vert = \sqrt{(2)^2+(-\frac{1}{2})^2} = \sqrt{4+\frac{1}{4}} = \sqrt{\frac{17}{4}} = \dfrac{\sqrt{17}}{2}$
$c.) \ \vert\vert u+v\vert\vert = \sqrt{(1+2)^2+(\frac{1}{2}-\frac{1}{2})^2} = \sqrt{(3)^2+(0)^2}=\sqrt{9+0}=\sqrt{9}=3$
