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CBSE Class 12 Mathematics 2026 Main Paper 65/4/1 · Q355 Marksline_intersection

CBSE Class 12 Mathematics 2026 Main Paper 65/4/1 · Question 35 (Three Dimensional Geometry)

Find the vector and Cartesian equations of the line parallel to (3,2,−8) through the intersection of (x−1)/2=(y−2)/3=(z−3)/4 and (x−4)/5=(y−1)/2=z.

✅ Step-by-Step Solution

Final Answer: r=(−1,−1,−1)+t(3,2,−8); (x+1)/3=(y+1)/2=(z+1)/(−8).
  1. Parametrize the two given lines by (1+2s,2+3s,3+4s) and (4+5u,1+2u,u).
  2. Matching coordinates gives s=u=−1 and intersection (−1,−1,−1).
  3. Use the specified direction through that point to get the vector and Cartesian forms.

📋 CBSE Stepwise Marking Scheme

  • [1 mark] Parametrize the two given lines by (1+2s,2+3s,3+4s) and (4+5u,1+2u,u).
  • [3 marks] Matching coordinates gives s=u=−1 and intersection (−1,−1,−1).
  • [1 mark] Use the specified direction through that point to get the vector and Cartesian forms.

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All Questions in CBSE Class 12 Mathematics 2026 Main Paper 65/4/1

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