If the vectors a =λ i +μ j +4 k, b =-2 i +4 j -2 k and c =2 i +3 j + k are coplanar and the projection of a on the vector b is √ 54 units, then the…

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