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:
The equation of line AB is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\displaystyle\frac{x-2}{2}=\frac{y-1}{3}=\frac{z-3}{-3}\)
The plane through P, Q and R is
\(2x+3y-3z = 5\)
(normal \(\overrightarrow{PQ}\times\overrightarrow{PR} = -2\hat{\imath}-3\hat{\jmath}+3\hat{k}\), through P(1, 1, 0)).
AB is the shortest distance from A to the plane, so AB is perpendicular to the plane: its direction ratios are those of the normal, 2, 3, −3. The line through A(2, 1, 3) is
\( \displaystyle \frac{x-2}{2}=\frac{y-1}{3}=\frac{z-3}{-3} \)
Note: This topic was not in the CUET 2026 syllabus.