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