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CBSE Class 12 Mathematics 2026 Main Paper 65/1/1 · Q232 Marksvector_algebra

CBSE Class 12 Mathematics 2026 Main Paper 65/1/1 · Question 23 (Vector Algebra)

Find the vector of magnitude 14 in the direction of QP, where P and Q are the points (1, 3, 2) and (−1, 0, 8) respectively.

✅ Step-by-Step Solution

Final Answer: 4î + 6ĵ − 12k̂
  1. QP = P − Q = (1−(−1), 3−0, 2−8) = (2, 3, −6).
  2. |QP| = √(4+9+36) = √49 = 7. Unit vector in direction QP = (2/7, 3/7, −6/7). Required vector = 14 × unit = (4, 6, −12) = 4î + 6ĵ − 12k̂.
  3. 4î + 6ĵ − 12k̂

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] QP = P − Q = (1−(−1), 3−0, 2−8) = (2, 3, −6).
  • [1 mark] |QP| = √(4+9+36) = √49 = 7. Unit vector in direction QP = (2/7, 3/7, −6/7). Required vector = 14 × unit = (4, 6, −12) = 4î + 6ĵ − 12k̂.
  • [0.5 marks] 4î + 6ĵ − 12k̂

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