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Let ABC be a triangle such that BC = a, CA = b, AB = c, |a| = 6√2, |b| = 2√3 and b · c = 12. Consider the statements: (S1): |(a × b) + (c × b)| - |c| = 6(2√2 - 1) (S2): ∠ABC = cos⁻¹(√2/3) Then

1. both (S1) and (S2) are true
2. only (S1) is true
3. only (S2) is true
4. both (S1) and (S2) are false

Correct answer: both (S1) and (S2) are false

Solution

Both statements are false because the calculations involving the magnitudes and angles in the triangle do not satisfy the given conditions, indicating that the relationships derived from the triangle's sides and angles are incorrect.

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