Find a unit vector perpendicular to both the vectors \( (2 \hat{i}+3 \hat{j}+\hat{k}) \) and \( ...

Find a unit vector perpendicular to both the vectors \( (2 \hat{i}+3 \hat{j}+\hat{k}) \) and \( (\hat{i}-\hat{j}+2 \hat{k}) \).
a. \( \frac{1}{\sqrt{8}}(4 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-5 \hat{\mathrm{k}}) \)
b. \( \frac{1}{\sqrt{83}}(7 \hat{i}-3 \hat{j}-5 \hat{k}) \)
c. \( \frac{1}{\sqrt{8}}(4 \hat{i}+3 \hat{j}+1 \hat{k}) \)
d. None of these