Vectors a, b and c are such that a + b + c = 0 and |a| = 3, |b| = 5 and |c| = 7. Find the angle between a and b.

Given a + b + c = 0
|a| = 3, |b| = 5, |c| = 7
a + b = -c
(a + b) · (a + b) = (-c) · (-c)
a · a + a · b + a · b + b · b = |c|^2
|a|^2 + 2a · b + |b|^2 = |c|^2
9 + 2(3)(5)cosθ + 25 = 49
30cosθ = 49 - 34
30cosθ = 15
cosθ = 1/2
θ = π/3