JEE Main 2024 Mathematics question
Let a⃗ and b⃗ be two vectors such that |a⃗| = 1, |b⃗| = 4, and a⃗·b⃗ = 2. If c⃗ = (2a⃗ × b⃗) − 3b⃗ and the angle between b⃗ and c⃗ is α, then 192 sin²α is equal to .
Answer: 48
Solution
|c⃗|² = 4|a⃗ × b⃗|² + 9|b⃗|² = 4(16 − 4) + 144 = 192 (the cross term vanishes since 2a⃗ × b⃗ ⊥ b⃗).
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