Answer
$|\overrightarrow{u}|=\sqrt {29}$;
$\overrightarrow{u}+\overrightarrow{v}=\lt 2,-2 \gt $;
$\overrightarrow{u} -\overrightarrow{v} =\lt -8,-2 \gt $;
$2 \overrightarrow{u} =\lt 10,-4 \gt $
and
$3\overrightarrow{u} -2\overrightarrow{v}=\lt 21,-6 \gt$
Work Step by Step
$|\overrightarrow{u}|=\sqrt {(5)^2+(-2)^2}=\sqrt {25+4}=\sqrt {29}$;
$\overrightarrow{u}+\overrightarrow{v}=\lt 5,-2 \gt + \lt -3,0\gt=\lt 5-3,-2+0 \gt =\lt 2,-2 \gt$;
$\overrightarrow{u} -\overrightarrow{v}=\lt 5,-2 \gt - \lt -3,0\gt=\lt 5-(-3),-2 -0 \gt =\lt -8,-2 \gt $;
$2 \overrightarrow{u}=2\lt 5,-2 \gt =\lt 10,-4 \gt $
and
$3\overrightarrow{u} -2\overrightarrow{v}=3\lt 5,-2 \gt -2 \lt -3,0\gt=\lt 15,-6\gt +\lt 6,0\gt=\lt 21,-6 \gt$
