Question

A unit vector making an obtuse angle with x – axis and perpendicular to the plane containing the points $\hat{i}-2\hat{j}+3\hat{k},2\hat{i}-3\hat{j}+4\hat{k}$ and $\hat{i}-5\hat{j}+7\hat{k}$,

• A. Also makes and obtuse angle with y - axis
• B. Also makes an obtuse angle with z - axis
• C. Also makes an obtuse angle with y and z axis
• D. None of the above

Answer 1

The correct option is B Also makes an obtuse angle with z - axis

Let the given points be A, B and C respectively. The unit vectors perpendicular to the plane containing A, B and C are given by
$\pm \frac{\overrightarrow{AB}\times \overrightarrow{AC}}{|\overrightarrow{AB}\times \overrightarrow{AC}|}=\pm \frac{1}{\sqrt{26}}(\hat{i}-4\hat{j}+3\hat{k})$
Since the required vector makes an obtuse angle with x – axis. So, it is equal to $\frac{-1}{\sqrt{26}}(\hat{i}-4\hat{j}+3\hat{k})$. Clearly it also makes an obtuse angle with z - axis.