If the components of \(\overrightarrow{\mathrm{a}}=\alpha \hat{i}+\beta \hat{j}+\gamma \hat{k}\) along and perpendicular…

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

[JEE Main 2025, 28 Jan (Shift 2)]