Let a and b are two vectors of magnitude 4 inclined at an angle π/3, then what is the angle between a and a – b?

|a| = |b| = 4, angle between a and b is π/3, so a·b = 16·cos(π/3) = 8. |a – b|² = |a|² + |b|² – 2a·b = 16 + 16 – 16 = 16, so |a – b| = 4. cos(angle between a and a – b) = (a·(a – b))/(|a|·|a – b|) = (|a|² – a·b)/(4·4) = (16 – 8)/16 = 1/2. So the angle is π/3. Hmm, that gives π/3, option (b). Let me recheck — a·(a – b) = a·a – a·b = 16 – 8 = 8. Denominator = 4·4 = 16. cos = 8/16 = 1/2, angle = π/3. The answer is π/3.