If \( A B C D \) is parallelogram, \( A B=2 \hat{i}+4 \hat{j}-5 \hat{k} \) and \( A D=\hat{i}+2 ...

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If \( A B C D \) is parallelogram, \( A B=2 \hat{i}+4 \hat{j}-5 \hat{k} \) and \( A D=\hat{i}+2 \hat{j}+3 \hat{k} \) then the unit vectors in the direction of \( B D \) is
(a) \( \frac{1}{\sqrt{69}}(\hat{i}+2 \hat{j}-8 \hat{k}) \)
(b) \( \frac{1}{69}(\hat{i}+2 \hat{j}-8 \hat{k}) \)
(c) \( \frac{1}{\sqrt{69}}(-\hat{i}-2 \hat{j}-8 \hat{k}) \)
(d) \( \frac{1}{69}(-\hat{i}-2 \hat{j}+8 \hat{k}) \)
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