Answer
$62\ m$
Work Step by Step
We have:
$\vec{a} = 43.30\ m\ \hat{i}+ 25\ m\ \hat{j}$
$\vec{b} = -48.30\ m\ \hat{i}+(-12.94\ m)\ \hat{j}$
$\vec{c} = 35.35\ m\ \hat{i}+(-35.35\ m)\ \hat{j}$
Given that the condition is ($\vec{a}+ \vec{b})-(\vec{c}+\vec{d})=0$.
From this, the value of $\vec{d}$ is
$\vec{d} = \vec{a}+\vec{b}-\vec{c}$
Therefore;
$ \vec{a}+\vec{b}-\vec{c}= 43.30\ m\ \hat{i}+ 25\ m\ \hat{j}-48.30\ m\ \hat{i}-12.94\ m\ \hat{j}-35.35\ m\ \hat{i}+35.35\ m\ \hat{j}$
$\vec{d}=(-40.4\hat{i}+47.4\hat{j})\ m $
$|\vec{d}| = \sqrt {40.4^2+47.4^2} = 62\ m $
