If a → = i ^ + 2 j ^ + 3 k ^ , b → = - i ^ + 2 j ^ + k ^ , c → = 3 i ^ + j ^ and a → + p b → is normal to c → , then p is equal to

Question

If a → = i ^ + 2 j ^ + 3 k ^ , b → = - i ^ + 2 j ^ + k ^ , c → = 3 i ^ + j ^ and a → + p b → is normal to c → , then p is equal to, 0, 1, 5, 3

MARKS App · Accepted Answer

a → + p b → is normal to c → ∴ a → + p b → · c → = 0 1 - p i ^ + 2 + 2 p j ^ + 3 + p k ^ · 3 i ^ + j ^ = 0 3 - 3 p + 2 + 2 p = 0 ⇒ p = 5