Question

The vectors perpendicular to $\hat{i}-\hat{j}-\hat{k}$ in the plane of $\hat{i}-\hat{j}-\hat{k}$ and $-\hat{i}+\hat{j}+\hat{k}$ are

• A. $2\hat{i}+\hat{j}+\hat{k}$
• B. $-4\hat{i}-2\hat{j}-2\hat{k}$
• C. $4\hat{i}+2\hat{j}+2\hat{k}$
• D. All the above

Answer 1

Answer: (D)

All the above

$\overline{i}-\overline{j}-\overline{k}=-(-\overline{i}+\overline{j}+\overline{k})$ ...(i)

Thus the above two vectors are anti-parallel and the normal to the plane is given by

$\overline{i}-\overline{j}-\overline{k}$

Hence the required vectors have to be perpendicular to the normal vector.

As we can observe all of the above options give

$\overline{V}.(\overline{i}-\overline{j}-\overline{k})=0$

Hence the correct answer is all of the above.