If a⃗ + b⃗ + c⃗ = 0⃗ and |a⃗| = 3, |b⃗| = 5 and |c⃗| = 7, then the angle between a⃗ and b⃗ isयदि a⃗ + b⃗ + c⃗ = 0⃗ तथा |a⃗| = 3, |b⃗| = 5 और |c⃗| = 7, तब a⃗ तथा b⃗ के बीच बना कोण है

Explanation

c⃗ = −(a⃗ + b⃗), so |c⃗|² = |a⃗|² + |b⃗|² + 2a⃗·b⃗, i.e. 49 = 9 + 25 + 2a⃗·b⃗, giving a⃗·b⃗ = 15/2. Then cos θ = (15/2)/(3·5) = 1/2, so θ = π/3.c⃗ = −(a⃗ + b⃗), इसलिए |c⃗|² = |a⃗|² + |b⃗|² + 2a⃗·b⃗, अर्थात् 49 = 9 + 25 + 2a⃗·b⃗, जिससे a⃗·b⃗ = 15/2। तब cos θ = (15/2)/(3·5) = 1/2, अतः θ = π/3।