Let $a=2\overline{i}+\overline{j}-\overline{k}$ and $b=\overline{i}+3\overline{j}-5\overline{k}$ be two vectors and $\overline{r}$ be a vector along the vector $3\overline{\mathrm{a}}–2\overline{\mathrm{b}}$ such that $\left|\overline{r}\right|=\sqrt{74}.$If the direction of $\overline{r}$  is opposite to that of  $3\overline{\mathrm{a}}–2\overline{\mathrm{b}}$ then $\overline{\mathrm{r}}=$

Given $\overline{a}=2\overline{i}+\overline{j}-\overline{k}$ and $\overline{b}=\overline{i}+3\overline{j}-5\overline{k}$ Now 
$3\overline{a}-2\overline{b}=(6\overline{i}+3\overline{j}-3\overline{k})$
$-(2\overline{\mathrm{i}}+6\overline{\mathrm{j}}-10\overline{\mathrm{k}})=4\overline{\mathrm{i}}-3\overline{\mathrm{j}}+7\overline{\mathrm{k}}$
The direction of $\overline{r}$  is opposite to the direction of  .
So 
$\overline{r}=-\left(3\overline{a}-2\overline{b}\right)$
$=-(4\overline{i}-3\overline{j}+7\overline{k})=-4\overline{i}+3\overline{j}-7\overline{k}$