Let a → , b → and c → , be three unit vectors such that a → + b → + c → = 0 → . If λ = a → ⋅ b → + b → ⋅ c → + c → ⋅ a → and d → = a → × b → + b → × c → + c → × a → , then the order pair, λ , d → , is equal to.

Step-by-step solution

a → + b → + c → 2 = 0 3 + 2 a → · b → + b → · c → + c → · a → = 0 a → · b → + b → · c → + c → · a → = - 3 2 ⇒ λ = - 3 2 d → = a → × b → + b → × - a → - b → + - a → - b → × a → = a → × b → + a → × b → + a → × b → d → = 3 a → × b → .