If $\overrightarrow {a}=\hat i+\hat j-\hat k$ and $\overrightarrow{b} =+ \lambda \hat i- 3\hat j+\hat k$ and the orthogonal projection of $\overrightarrow b$ on $\overrightarrow a $ is $\large\frac{4}{3}$$ (\hat i-\hat j-\hat k)$, then $\lambda$ is equal to

Question

\[\begin {array} {1 1} (a)\;0 & \quad (b)\;2 \\ (c)\;12 & \quad (d)\;-1 \end {array}\]