Let a, b c R be 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 i + b j + c k and b i + c j + a k is:

Vector Algebra: JEE Main 2020 Mathematics question

JEE Main 2020 · 3 Sep, Evening shift · Q5773

JEE Main 20203 Sep, Evening shiftMathematicsHardVector Algebra184× since 2002

Let a, b c

\in

R be such that a² + b² + c² = 1. If

a\cos \theta = b\cos \left( {\theta + {{2\pi } \over 3}} \right) = c\cos \left( {\theta + {{4\pi } \over 3}} \right)

, where

{\theta = {\pi \over 9}}

, then the angle between the vectors

a\widehat i + b\widehat j + c\widehat k

and

b\widehat i + c\widehat j + a\widehat k

is :