I can't finish this attached vectors question.
Dear Stuck Man,
There is a calculation error in your result for $\displaystyle \overline{PQ}$. It must be, $\displaystyle \overline{PQ}=\frac{1}{2}\underline{b}-\frac{3}{10}\underline{a}$.
After you correct this you can equate the two results you obtained for $\displaystyle \overline{QR}$. Then considering the coefficients of $\displaystyle \underline{a}~and~\underline{b}$ you can find k and n.
Hope this will help you.