Answer
$|\overrightarrow{u}|=\sqrt {13}$;
$\overrightarrow{u}+\overrightarrow{v} =\lt 6,4 \gt $;
$\overrightarrow{u} -\overrightarrow{v}=\lt -10,2 \gt$;
$2 \overrightarrow{u}=\lt -4,6 \gt $
and
$3\overrightarrow{u} -2\overrightarrow{v}=\lt -22,7\gt$
Work Step by Step
$|\overrightarrow{u}|=\sqrt {(-2)^2+(3)^2}=\sqrt {4+9}=\sqrt {13}$;
$\overrightarrow{u}+\overrightarrow{v}=\lt-2,3 \gt + \lt 8, 1\gt=\lt -2+8,3+1\gt =\lt 6,4$;
$\overrightarrow{u} -\overrightarrow{v}=\lt-2,3 \gt - \lt 8, 1\gt=\lt -2 -8,3 -1\gt =\lt -10,2 \gt$;
$2 \overrightarrow{u}=2\lt-2,3 \gt =\lt -4,6 \gt $
and
$3\overrightarrow{u} -2\overrightarrow{v}=3\lt-2,3 \gt -2 \lt 8, 1\gt=\lt -6,9\gt +\lt -16, 2\gt=\lt -22,7\gt$
