Let a → = i ^ + j ^ + 2 k ^ , b → = b 1 i ^ + b 2 j ^ + 2 k ^ and c → = 5 i ^ + j ^ + 2 k ^ be three vectors such that the projection vector of b → on a → is a → . If a → + b → is perpendicular to c → , then b → is equal to:

Step-by-step solution

Since a → + b → is perpendicular to c → , hence a → + b → · c → = 0 ⇒ a → · c → + b → · c → = 0 ⇒ 5 + 1 + 2 + 5 b 1 + b 2   + 2 = 0 ⇒ 5 b 1 + b 2 = - 10               . . . 1 Given, b → · a → a → = a → ∵ p → = r i ^ + s j ^ + t k ^ ⇒ p → = r 2 + s 2 + t 2 ⇒ b 1 + b 2 + 2 = 4 ⇒ b 1 + b 2 = 2       . . . 2 S