The unit vector which is orthogonal to the vector $5 \hat{i}+2 \hat{j}+6 \hat{k}$ and is coplanar with the vectors $2 \hat{i}+\hat{j}+\hat{k}$ and $\hat{i}-\hat{j}+\hat{k}$ is
- A$\frac{2 \hat{i}-6 \hat{j}+\hat{k}}{\sqrt{41}}$
- B$\frac{2 \hat{i}-5 \hat{j}}{\sqrt{29}}$
- C$\frac{-3 \hat{\mathrm{j}}+\hat{\mathrm{k}}}{\sqrt{10}}$
- D$\frac{2 \hat{\mathrm{i}}-8 \hat{\mathrm{j}}+\hat{\mathrm{k}}}{69}$
✓ Correct answer: C
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