If $\overrightarrow {a} = \hat{i} + 2\hat{j} + 3\hat{k}$ and $\overrightarrow {b} = 2\hat{i} + 4\hat{j} - 5\hat{k}$ represents two adjacent sides of a parallelogram, find unit vectors parallel to the diagonals of the parallelogram.

Question

$(A)\; \frac{1}{7} (3\hat{i} - 6\hat{j} -2\hat{k}),$$\frac{1}{\sqrt{69} }(\hat{i}-2\hat{j} -8\hat{k})$
$(B) \; \frac{1}{7} (3\hat{i} +6\hat{j} -2\hat{k}), \frac{1}{\sqrt{69}} (\hat{i} + 2\hat{j} +8\hat{k})$
$(C)\; \frac{1}{7} (3\hat{i}+6\hat{j} - 2\hat{k}) , \frac{1}{\sqrt{69} } (\hat{i} +2\hat{j} - 8\hat{k})$
$(D)\; \frac{1}{7}(3\hat{i} + 6\hat{j} +2\hat{k}), \frac{1}{\sqrt{69} } (\hat {i} - 2\hat{j} -8\hat{k})$