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: