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Between the following two statements : Statement-I : Let a = i + 2j - 3k and b = 2i + j - k. Then the vector r satisfying a × r = a × b and a · r = 0 is of magnitude √10. Statement-II : In a triangle ABC, cos2A + cos2B + cos2C ≥ 3/2.

1. Both Statement-I and Statement-II are incorrect
2. Statement-I is incorrect but Statement-II is correct
3. Both Statement-I and Statement-II are correct
4. Statement-I is correct but Statement-II is incorrect

Correct answer: Statement-I is incorrect but Statement-II is correct

Solution

Statement-I is incorrect because the conditions given do not yield a vector r of the specified magnitude, while Statement-II is correct as it reflects a known inequality in triangle geometry, where the sum of the squares of the cosines of the angles is always greater than or equal to 3/2.

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