Let ^a and ^b be two unit vectors. If the vectors c = ^a + 2^b and d = 5^a - ^b are perpendicular to each other, then the angle between ^a and ^b is

Given that c and d are Perpendicular
∴ c . d = 0
Putting values ⇒ 5|^a|^2 + 6^a.^b - |^b|^2 = 0
⇒ 6^a . ^b = -5
⇒ ^a . ^b = -5/6 = |^a||^b|cosθ = -1/2
Since ^a and ^b are Unit vectors
So, cosθ = -1/2
∴ θ = π/3
Hence, option 'D' is correct.