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CBSE Class 12 Mathematics 2026 Main Paper 65/1/2 · Q335 Marksline_intersection

CBSE Class 12 Mathematics 2026 Main Paper 65/1/2 · Question 33 (Three Dimensional Geometry)

Show that the line through A=(0,−1,−1), B=(4,5,1) intersects the line through C=(3,9,4), D=(−4,4,4). Find the line through the intersection and the origin.

✅ Step-by-Step Solution

Final Answer: Intersection (10,14,4), required line r=t(5,7,2).
  1. Parametrize AB by (2s,3s−1,s−1) and CD by (3−7u,9−5u,4).
  2. Equating z gives s=5. Equating x gives u=−1. Both y-coordinates are then 14, and both x-coordinates are 10.
  3. The intersection is (10,14,4), so a direction from the origin is (5,7,2). The required equation is r=t(5,7,2).

📋 CBSE Stepwise Marking Scheme

  • [1 mark] Parametrize AB by (2s,3s−1,s−1) and CD by (3−7u,9−5u,4).
  • [3 marks] Equating z gives s=5. Equating x gives u=−1. Both y-coordinates are then 14, and both x-coordinates are 10.
  • [1 mark] The intersection is (10,14,4), so a direction from the origin is (5,7,2). The required equation is r=t(5,7,2).

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All Questions in CBSE Class 12 Mathematics 2026 Main Paper 65/1/2

Q1Q2Q3Q4Q5Q6Q7Q8Q9Q10Q11Q12Q13Q14Q15Q16Q17Q18Q19Q20Q21Q22Q23Q24Q25Q26Q27Q28Q29Q30Q31Q32Q33Q34Q35Q36Q37Q38

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