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CBSE Class 12 Mathematics 2026 Main Paper 65/1/3 · Q325 Marksparallel_line_distance

CBSE Class 12 Mathematics 2026 Main Paper 65/1/3 · Question 32 (Three Dimensional Geometry)

Show that the line through (0,4,1) and (2,3,−1) is parallel to the line through (4,5,0) and (2,6,2). Find their distance.

✅ Step-by-Step Solution

Final Answer: Parallel, distance 3.
  1. Their directions are u=(2,−1,−2) and −u=(−2,1,2), so they are parallel.
  2. The displacement between the first points is w=(4,1,−1). Its cross product with u is (−3,6,−6), with norm 9.
  3. Divide the cross-product norm by the direction norm 3 to get distance 3.

📋 CBSE Stepwise Marking Scheme

  • [1 mark] Their directions are u=(2,−1,−2) and −u=(−2,1,2), so they are parallel.
  • [3 marks] The displacement between the first points is w=(4,1,−1). Its cross product with u is (−3,6,−6), with norm 9.
  • [1 mark] Divide the cross-product norm by the direction norm 3 to get distance 3.

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

Q1Q2Q3Q4Q5Q6Q7Q8Q9Q10Q11Q12Q13Q14Q15Q16Q17Q18Q19Q20Q21Q22Q23Q24Q25Q26Q27Q28Q29Q30Q31Q32Q33Q34Q35Q36Q37Q38

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