What is the angle between a and c?

Similarly, since |b| = |c| = |b+c| = 1, the angle between b and c is 2π/3. Also |a+b+c| = 1 gives |a+b+c|² = |a|² + |b|² + |c|² + 2(a·b + b·c + a·c) = 3 + 2(−1/2 − 1/2 + a·c) = 1. So 3 + 2(−1) + 2a·c = 1, giving 1 + 2a·c = 1, a·c = 0. Wait, that gives π/2. Let me recompute: 3 − 2 + 2a·c = 1, so 1 + 2a·c = 1, a·c = 0, meaning angle = π/2. The official answer is π/2, option (c).