If ABCD is a parallelogram, vector AB = 2i + 4j - 5k and vector AD = i + 2j + 3k, then the unit vector in the direction of BD is
\(\frac{1}{√69}(\hat{i}+2\hat{j}-8\hat{k})\)
\(\frac{1}{69}(\hat{i}+2\hat{j}-8\hat{k})\)
\(\frac{1}{√69}(\hat{-i}-2\hat{j}+8\hat{k})\)
\(\frac{1}{69}(\hat{-i}-2\hat{j}+8\hat{k})\)
The correct answer is option C) \(\frac{1}{√69}(\hat{-i}-2\hat{j}+8\hat{k})\)
The respective values of \( |\vec{a}| \) and} \( |\vec{b}| \), if given \[ (\vec{a} - \vec{b}) \cdot (\vec{a} + \vec{b}) = 512 \quad \text{and} \quad |\vec{a}| = 3 |\vec{b}|, \] are: