Answer
$\vec{r}=(9.0 \mathrm{m}) \hat{\mathrm{i}}+(6.0 \mathrm{m}) \hat{\mathrm{j}}+(-7.0 \mathrm{m}) \hat{\mathrm{k}}$
Work Step by Step
$\text{The three vectors are}$ $\begin{aligned} \vec{d}_{1} &=4.0 \hat{\mathrm{i}}+5.0 \hat{\mathrm{j}}-6.0 \hat{\mathrm{k}} \\ \vec{d}_{2} &=-1.0 \hat{\mathrm{i}}+2.0 \hat{\mathrm{j}}+3.0 \hat{\mathrm{k}} \\ \vec{d}_{3} &=4.0 \hat{\mathrm{i}}+3.0 \hat{\mathrm{j}}+2.0 \hat{\mathrm{k}} \end{aligned}$ $therefore$ $\vec{r}=\vec{d}_{1}-\vec{d}_{2}+\vec{d}_{3}=(9.0 \mathrm{m}) \hat{\mathrm{i}}+(6.0 \mathrm{m}) \hat{\mathrm{j}}+(-7.0 \mathrm{m}) \hat{\mathrm{k}}$
