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CBSE Class 12 Mathematics 2026 Main Paper 65/1/3 · Q242 Markstriangle_area

CBSE Class 12 Mathematics 2026 Main Paper 65/1/3 · Question 24 (Vector Algebra)

Using vectors, find the area of the triangle with A=(1,2,3), B=(2,−1,4), and C=(4,5,−1).

✅ Step-by-Step Solution

Final Answer: √274/2
  1. Use half the magnitude of AB×AC, where AB=(1,−3,1) and AC=(3,3,−4).
  2. The cross product is (9,7,12), of norm √(81+49+144).
  3. Thus the area is √274/2 square units.

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] Use half the magnitude of AB×AC, where AB=(1,−3,1) and AC=(3,3,−4).
  • [1 mark] The cross product is (9,7,12), of norm √(81+49+144).
  • [0.5 marks] Thus the area is √274/2 square units.

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

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