If the components of a =α i +β j +γ k along and perpendicular to b =3 i + j - k respectively, are 16/11(3 i + j - k ) and 1/11(-4 i -5 j -17 k ),…

If the components of $\displaystyle \overrightarrow{\mathrm{a}}=\alpha \hat{i}+\beta \hat{j}+\gamma \hat{k}$ along and perpendicular to $\displaystyle \overrightarrow{\mathrm{b}}=3 \hat{i}+\hat{j}-\hat{k}$ respectively, are $\displaystyle \frac{16}{11}(3 \hat{i}+\hat{j}-\hat{k})$ and $\displaystyle \frac{1}{11}(-4 \hat{i}-5 \hat{j}-17 \hat{k})$, then $\displaystyle \alpha^2+\beta^2+\gamma^2$ is equal to :