Given a → = 3 i ^ - j ^ , b → = 2 i ^ + j ^ - 3 k ^ and b → = b 1 → + b 2 → , where b 1 → is parallel to a → and b 2 → is perpendicular to a → then b 2 → is equal to

Step-by-step solution

Given:- a → = 3 i ^ - j ^ and b → = 2 i ^ + j ^ - 3 k ^ Also, b → = b 1 → + b 2 → where b 1 → ∥ a → ∵   b 1 → ∥ a → ∴   b 1 → = λ 3 i ^ - j ^ Let b 2 → = x i ^ + y j ^ + z k ^ ∵   b 2 → ⊥ a → ∴   b 2 → . a → = 0 ⇒   3 x - y = 0     . . . 1 As, b → = b 1 → + b 2 → 2 i ^ + j ^ - 3 k ^ = 3 λ + x i ^ + y - λ j ^ + z