If the vectors $$\vec{a} = \lambda\hat{i} + \mu\hat{j} + 4\hat{k}$$, $$\vec{b} = -2\hat{i} + 4\hat{j} - 2\hat{k}$$ and $$\vec{c} = 2\hat{i} + 3\hat{j} + \hat{k}$$ are coplanar and the projection of $$\vec{a}$$ on the vector $$\vec{b}$$ is $$\sqrt{54}$$ units, then the sum of all possible values of $$\lambda + \mu$$ is equal to

A

$$0$$

B

$$6$$

C

$$24$$

D

$$18$$