JEE Main 2024 Mathematics question
Let and be two vectors such that |a⃗| = 1, a⃗·b⃗ = 2 and |b⃗| = 4. If , then the angle between b⃗ and c⃗ is equal to :
Answer: (C)
Solution
|a⃗ × b⃗|² = |a|²|b|² − (a·b)² = 16 − 4 = 12. Then b⃗·c⃗ = −3|b|² = −48 and |c⃗|² = 4·12 + 9·16 = 192. So cosθ = −48/(4 × √192) = −√3/2.