A team of 5 persons goes on a rescue operation in a helicopter. They know the coordinates of places from where people need to be rescued. These are P(1, 1, 0), Q(1, 2, 1) and R(−2, 2, −1). They decide to stop at Point A (2, 1, 3). From A, 3 team members are dropped on ground using a rope. They reach the point B at the ground level so that distance AB is shortest from the plane passing through P, Q and R.
Based on the above information, answer the following:
How much distance a team member has to cover to reach point B from the helicopter?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\displaystyle\frac{7}{\sqrt{22}}\) units
The plane through P, Q and R is
\(2x+3y-3z-5 = 0\)
(normal \(\overrightarrow{PQ}\times\overrightarrow{PR} = -2\hat{\imath}-3\hat{\jmath}+3\hat{k}\), through P(1, 1, 0)).
AB is the perpendicular distance of A(2, 1, 3) from this plane:
\( \displaystyle AB = \frac{|2(2)+3(1)-3(3)-5|}{\sqrt{2^2+3^2+(-3)^2}} \)
\( \displaystyle = \frac{|-7|}{\sqrt{22}} = \frac{7}{\sqrt{22}} \text{ units} \)
Note: This topic was not in the CUET 2026 syllabus.