Answer
$a.) \ \vert \vert u \vert \vert = \sqrt{6}$
$b.) \ \vert \vert v \vert \vert = 2\sqrt{2}$
$c.) \ \vert\vert u+v\vert\vert = 3\sqrt{2} $
Work Step by Step
Given $u = (1,2,1)$ and $v = (0,2,-2)$
$a.) \ \vert \vert u \vert \vert = \sqrt{(1)^2+(2)^2+(1)^2} = \sqrt{1+4+1} = \sqrt{6}$
$b.) \ \vert \vert v \vert \vert = \sqrt{(0)^2+(2)^2+(-2)^2} = \sqrt{0+4+4} = \sqrt{8} = 2\sqrt{2}$
$c.) \ \vert\vert u+v\vert\vert = \sqrt{(1+0)^2+(2+2)^2+(1-2)^2} = \sqrt{(1)^2+(4)^2+(-1)^2} = \sqrt{1+16+1} = \sqrt{18} = 3\sqrt{2} $
