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CBSE Class 12 Mathematics 2026 Main Paper 65/5/3 · Q222 Marksline_angles

CBSE Class 12 Mathematics 2026 Main Paper 65/5/3 · Question 22 (Three Dimensional Geometry)

Find the acute angle between (x−2)/3=(y+5)/2=(1−z)/(−6) and (x−7)/1=y/2=(6−z)/(−2).

✅ Step-by-Step Solution

Final Answer: arccos(19/21).
  1. The two direction vectors are (3,2,6) and (1,2,2).
  2. Their dot product is 19 and their norms are 7 and 3.
  3. The cosine of the acute angle is 19/21.

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] The two direction vectors are (3,2,6) and (1,2,2).
  • [1 mark] Their dot product is 19 and their norms are 7 and 3.
  • [0.5 marks] The cosine of the acute angle is 19/21.

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All Questions in CBSE Class 12 Mathematics 2026 Main Paper 65/5/3

Q1Q2Q3Q4Q5Q6Q7Q8Q9Q10Q11Q12Q13Q14Q15Q16Q17Q18Q19Q20Q21Q22Q23Q24Q25Q26Q27Q28Q29Q30Q31Q32Q33Q34Q35Q36Q37Q38

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