3D Geometry
Three Dimensional Geometry
nta_pyq_2025_jan
Grade 12
Question:
Let the distance between two parallel lines be 5 units and a point P lie between the lines at a unit distance from one of them. An equilateral triangle P QR is formed such that Q lies on one of the parallel lines, while R lies on the other. Then (QR) is equal to _______ -. 2
Step-by-Step Solution
Key Concept: Apply the core result for lines and planes in three dimensions and simplify using the given constraints.
(28) P R = cosec \theta, P Q = 4 sec(30 + \theta) For equilateral d = PR = PQ ∘ \Rightarrow cos(\theta + 30 ) = 4 sin \theta \sqrt3 1 \Rightarrow cos \theta - sin \theta = 4 sin \theta 2 2 1 \Rightarrow tan \theta = 3\sqrt 3 2 2 2 QR = d = cosec \theta = 28
Correct Answer: 28