Maths · Coordinate geometry · chapter 11 of 14
Class 11 Maths Chapter 11: Introduction to Three Dimensional Geometry case study question with answers
One case-based question of the kind CBSE-pattern school exams ask: a passage, then 3 parts worth 4 marks in all, with the answer and the marking scheme for each. Written from the NCERT chapter.
Case study · 4 marks
A drone is tested inside an empty indoor hall in Bengaluru that is a cuboid 10 m long, 8 m wide and 6 m high. The engineers take one corner of the floor as the origin O, the floor as the XY-plane and the two walls meeting at O as the YZ-plane and the ZX-plane, with the hall in octant I and all distances in metres. The drone's position at any moment is recorded as three numbers, its distances from the two walls and its height above the floor, and the flight log stores these positions.
Part 1 · 1 mark
The corner of the ceiling diagonally opposite O has coordinates
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Answer: (c) (10, 8, 6)
That corner is 10 m from the YZ-plane wall, 8 m from the ZX-plane wall and 6 m above the floor: (10, 8, 6).
Part 2 · 1 mark
At one moment the log reads Q(0, 5, 3). At that moment the drone is
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Answer: (d) touching the wall in the YZ-plane
x = 0, so Q is of the form (0, y, z) and lies in the YZ-plane: the drone is at that wall, 5 m along it and 3 m up.
Part 3 · 2 marks
From Q(0, 5, 3) the drone flies in a straight line to R(4, 2, 3). Find the distance it flies.
Answer and marking scheme
QR = √((4 − 0)2 + (2 − 5)2 + (3 − 3)2) = √(16 + 9 + 0) = √25 = 5 m.
- distance formula with the two positions (1)
- QR = 5 m (1)
Or
A lamp hangs at L(2, 4, 5). Find its distance from the ceiling corner T(10, 8, 6).
Answer and marking scheme
LT = √((10 − 2)2 + (8 − 4)2 + (6 − 5)2) = √(64 + 16 + 1) = √81 = 9 m.
- distance formula with L and T (1)
- LT = 9 m (1)
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