## Fundamentals of Physics Extended (10th Edition)

$62\ m$
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; $\vec{a}+\vec{b}-\vec{c}= 43.30\ m\ \hat{i}+ 25\ m\ \hat{j}-48.30\ m\ \hat{i}-12.94\ m\ \hat{j}-35.35\ m\ \hat{i}+35.35\ m\ \hat{j}$ $\vec{d}=(-40.4\hat{i}+47.4\hat{j})\ m$ $|\vec{d}| = \sqrt {40.4^2+47.4^2} = 62\ m$