Let a → , b → and c → be three vectors such that a → = b → × b → × c → . If magnitudes of the vectors a → , b → and c → are 2 , 1 and 2 respectively and the angle between b → and c → is θ 0 < θ < π 2 , then the value of 1 + tan θ is equal to :

Step-by-step solution

We have, a → = b → · c → b → - b → · b → c → = 1 . 2 cos θ b → - c → ⇒ a → = 2 cos θ b → - c → a → 2 = 2 cos θ b → 2 + c → 2 - 2 . 2 cos θ b → · c → a → 2 = 2 cos θ 2 b → 2 + c → 2 - 2 . 2 cos θ b → · c → Given that, a → = 2 ,   b → = 1 and c → = 2 2 2 = 2 cos θ 2 + 2 2 - 2 . 2 cos θ b → &#18