Question

The adjacent sides of a parallelogram are $2\hat{i}+4\hat{j}-5\hat{k}$ and $\hat{i}+2\hat{j}+3\hat{k}$ then the unit vector parallel to a diagonal is

• A. $\frac{-\overline{i}-2\overline{j}+8\overline{k}}{\sqrt{69}}$
• B. $\frac{3\overline{i}+6\overline{j}-2\overline{k}}{7}$
• C. $\frac{\overline{i}+2\overline{j}-8\overline{k}}{\sqrt{69}}$
• D. All the above

Answer 1

The correct option is D All the above

As in this question direction of vector is not specified then it can be
$\pm \overrightarrow{a}\pm \overrightarrow{b}=$ Diagonal Vectors
Diagonal vector =$\frac{\overrightarrow{a}+\overrightarrow{b}}{|\overrightarrow{a}+\overrightarrow{b}|}=\frac{3i+6\hat{j}-2\hat{k}}{\sqrt{49}}$
or $\frac{\overrightarrow{a}-\overrightarrow{b}}{|\overrightarrow{a}-\overrightarrow{b}|}=\frac{i+2\hat{j}-8\hat{k}}{\sqrt{69}}$

or $\frac{\overrightarrow{-a}+\overrightarrow{b}}{|\overrightarrow{-a}+\overrightarrow{b}|}=\frac{-i-2\hat{j}+8\hat{k}}{\sqrt{69}}$