Let a → , b → , c → be three coplanar concurrent vectors such that angles between any two of them is same. If the product of their magnitudes is 14 and a → × b → · b → × c → + b → × c → · c → × a → + c → × a → · a → × b → = 168 then a → + b → + c → is equal to

Step-by-step solution

Given, product of magnitudes is 14 So, a → b → c → = 14 Also given angles between any two of them is same So, angle between a →   &   b → = b →   &   c → = c →   &   a → = θ = 2 π 3 So, a → . b → = - 1 2 a b ,   b → . c → = - 1 2 b c   &   a → . c → = - 1 2 a c Now solving a → × b → · b → × c → = a → · b &#8