Answer
$(-5.0\,m)\hat{i}+(2.0\,m)\hat{j}+(3.0\,m)\hat{k}$
Work Step by Step
$\vec{a}-\vec{b}=(4.0\,m-(-1.0\,m))\hat{i}-(3.0\,m-1.0\,m)\hat{j}+(1.0\,m-4.0\,m)\hat{k}$
$=(5.0\,m)\hat{i}-(2.0\,m)\hat{j}-(3.0\,m)\hat{k}$
Given that $\vec{a}-\vec{b}+\vec{c}=0$. Therefore
$\vec{c}$ is antiparallel and equal in magnitude to $\vec{a}-\vec{b}$.
$\vec{c}$ is obtained by changing the sign of scalar components of unit vectors $\hat{i},\,\hat{j}$ and $\hat{k}$
That is, $\vec{c}=(-5.0\,m)\hat{i}+(2.0\,m)\hat{j}+(3.0\,m)\hat{k}$
