Question

Let a, b,c ∈ R be the such that a² + b² + c² = 1. if a cos θ = b cos (θ + 2π/3) = c cos(θ + 4π/3), where θ = π/9, then the angle between the vectors a \(\hat{i}\)+ b\(\hat{j}\) + c\(\hat{k}\) and  b\(\hat{i}\)+ c\(\hat{j}\) + a\(\hat{k}\) is :

(1) \(\frac{π}{2}\)

(2) 0

(3) \(\frac{π}{9}\)

(4) \(\frac{2π}{3}\)

Answer 1

 (1) \(\frac{π}{2}\)