Let a → = 2 i ^ + j ^ + k ^ , and b → and c → be two nonzero vectors such that a → + b → + c → = a → + b → - c → and b → · c → = 0 . Consider the following two statement: A a → + λ c → ≥ a → for all λ ∈ ℝ . B a → and c → are always parallel

Step-by-step solution

Given, a → + b → + c → = a → + b → - c → Now squaring both side we get, ⇒ a → + b → + c → 2 = a → + b → - c → 2 ⇒ a → 2 + b → 2 + c → 2 + 2 a → · b → + 2 b → · c → + 2 c → · a → = a → 2 + b → 2 + c → 2 + 2 a → · b → - 2 b → · c → - 2 c → · a → ⇒ 2 b → · c → + 2 c → &#1