JEE MainHardQuestion 260012
Question
If a⃗ + b⃗ + c⃗ = 0 and |a⃗| = 3, |b⃗| = 5, |c⃗| = 7, then the angle between a⃗ and b⃗ is:
- A60°Correct
- B90°
- C120°
- D30°
Correct answer
60°
Explanation
a⃗ + b⃗ = −c⃗ → |a⃗+b⃗|² = |c⃗|² = 49. |a⃗|² + 2a⃗·b⃗ + |b⃗|² = 49 → 9 + 2a⃗·b⃗ + 25 = 49 → a⃗·b⃗ = 15/2. cos θ = (a⃗·b⃗)/(|a⃗||b⃗|) = (15/2)/(15) = 1/2 → θ = 60°.