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CBSE Class 12 Mathematics 2026 Main Paper 65/1/3 · Q201 Marksthree_dimensional_geometry

CBSE Class 12 Mathematics 2026 Main Paper 65/1/3 · Question 20 (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.

✅ Step-by-Step Solution

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

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All Questions in CBSE Class 12 Mathematics 2026 Main Paper 65/1/3

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