Answer
$\approx 13.45m$
Work Step by Step
$\overrightarrow {r}=\overrightarrow {a}+\overrightarrow {b}=(a_x\widehat {i}+a_{y}\widehat {j}+a_{z}\widehat {k})+(b_x\widehat {i}+b_{y}\widehat {j}+b_{z}\widehat {k}) $
$=\left( a_x+b_x\right) \widehat {i}+\left( a_y+b_y\right) \widehat {j}+\left( a_{z}+b_{z}\right) \widehat {k}$
$\Rightarrow r=\left( 4.0m+\left( -13.0m\right) \right) \widehat {i}+\left( 3.0m+7.0m\right) \widehat {j}=\left( -9.0m\right) \widehat {i}+\left( 10m\right) \widehat {j}$
So the magnitude of $r$ will be
$r=\sqrt {r_x^{2}+r_y^{2}}=\sqrt {\left( -9.0m\right) ^{2}+\left( 10.0m\right) ^{2}}\approx 13.45m$
