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For a triangle ABC, let p = BC, q = CA and r = BA. If |p| = 2√3, |q| = 2 and cosθ = 1/√3, where θ is the angle between p and q, then |p × (q − 3r)|^2 + 3|r|^2 is equal to: (1) 340 (2) 220 (3) 410 (4) 200

1. 340
2. 220
3. 410
4. 200

Correct answer: 200

Solution

The calculation involves using the properties of the cross product and the cosine of the angle between vectors. By substituting the given values into the formula, we find that the expression simplifies to 200, confirming that option D is correct.

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