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CBSE Class 12 Mathematics 2026 Main Paper 65/1/2 · Q191 Marksthree_dimensional_geometry

CBSE Class 12 Mathematics 2026 Main Paper 65/1/2 · Question 19 (Three Dimensional Geometry)

Assertion (A): Lines given by x = py + q, z = ry + s and x = p'y + q', z = r'y + s' are perpendicular to each other when pp' + rr' = 1. Reason (R): Two lines r = a₁ + λ b₁ and r = a₂ + μ b₂ are perpendicular to each other if b₁·b₂ = 0.

(A) Both A and R are true and R is the correct explanation of A
(B) Both A and R are true but R is NOT the correct explanation of A
(C) A is true and R is false
(D) A is false and R is true

✅ Step-by-Step Solution

Final Answer: (D) A is false and R is true

Direction vectors: (p,1,r) and (p',1,r').
Perpendicular if pp' + 1 + rr' = 0 ⇒ pp' + rr' = −1, not 1. So A false.
R is true (dot product of direction vectors zero).

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