JEE Main 2024 Mathematics question
Between the following two statements : Statement-I : Let a⃗ = î + 2ĵ − 3k̂ and b⃗ = 2î + ĵ − k̂. Then the vector r⃗ satisfying a⃗ × r⃗ = a⃗ × b⃗ and a⃗·r⃗ = 0 is of magnitude √10. Statement-II : In a triangle ABC, cos2A + cos2B + cos2C ≥ −3/2.
Answer: (B)
Solution
From a⃗ × (r⃗ − b⃗) = 0 we get r⃗ − b⃗ = λa⃗. Then a⃗·r⃗ = 0 gives a⃗·b⃗ + λ|a⃗|² = 0, with a⃗·b⃗ = 2 + 2 + 3 = 7 and |a⃗|² = 14, so λ = −1/2. Then r⃗ = b⃗ − a⃗/2 = (3î + k̂)/2 ... = (3/2, 0,
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