Let a → , b → , c → be three-unit vectors and a → · b → = a → · c → = 0 . If the angle between b → and c → is π 3 , then [ a → b → c → ] 2 =

Step-by-step solution

Given that a → · b → = a → · c → = 0 ⇒ a → is perpendicular to both b →   &   c → . The vector perpendicular to both b →   &   c → is b → × c → . Now, unit vector a → = b → × c → b → × c → . We know that, b → × c → 2 = b → 2 c → 2 - b → · c → 2 ⇒ b → × c → 2 = 1 · 1 - b → c → co