Let p =2 i -3 j - k, q =-3 i +4 j + k and r = i + j +2 k. Express r in the form of r =λ p +μ q and hence find the values of λ and μ.

Let $\displaystyle \overrightarrow{\mathrm{p}}=2 \hat{\mathrm{i}}-3 \hat{\mathrm{j}}-\hat{\mathrm{k}}, \overrightarrow{\mathrm{q}}=-3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+\hat{\mathrm{k}}$ and $\displaystyle \overrightarrow{\mathrm{r}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+2 \hat{\mathrm{k}}$. Express $\displaystyle \overrightarrow{\mathrm{r}}$ in the form of $\displaystyle \vec{\mathrm{r}}=\lambda \vec{\mathrm{p}}+\mu \vec{\mathrm{q}}$ and hence find the values of $\displaystyle \lambda$ and $\displaystyle \mu$.