MathematicsHard202×since 2002Q5773Let a, b c ∈\in∈ R be such that a² + b² + c² = 1. If acosθ=bcos(θ+2π3)=ccos(θ+4π3)a\cos \theta = b\cos \left( {\theta + {{2\pi } \over 3}} \right) = c\cos \left( {\theta + {{4\pi } \over 3}} \right)acosθ=bcos(θ+32π)=ccos(θ+34π), where θ=π9{\theta = {\pi \over 9}}θ=9π, then the angle between the vectors ai^+bj^+ck^a\widehat i + b\widehat j + c\widehat kai+bj+ck and bi^+cj^+ak^b\widehat i + c\widehat j + a\widehat kbi+cj+ak is :A0Bπ9{{\pi \over 9}}9πC2π3{{{2\pi } \over 3}}32πDπ2{{\pi \over 2}}2πCheck answerSkip