Let a → = 3 i ^ + 2 j ^ + k ^ , b → = 2 i ^ − j ^ + 3 k ^ and c → be a vector such that a → + b → × c → = 2 a → × b → + 24 j ^ − 6 k ^ and a → − b → + i ^ . c → = − 3 . Then c → 2 is equal to _______.

Step-by-step solution

Given, a → = 3 i ^ + 2 j ^ + k ^ , b → = 2 i ^ − j ^ + 3 k ^ and c → be a vector such that a → + b → × c → = 2 a → × b → + 24 j ^ − 6 k ^ Now, finding a → × b → = i ^ j ^ k ^ 3 2 1 2 - 1 3 = 7 i ^ − 7 j ^ − 7 k ^ Now, solving a → + b → × c → = 2 a → × b → + 24 j ^ − 6 k ^ ⇒ 5 i ^ + j ^ + 4 k ^ × c → = 2 7 i ^ − 7 j ^ − 7 k ^ + 24 j ^ − 6 k ^ ⇒ i ^ j ^ k ^ 5 1 4 x y z = 14 i ^ + 10 j ^ − 20 k ^ ⇒ i ^ z − 4 y − j ^ 5 z − 4 x + k ^ 5 y − x = 14 i ^ + 10 j ^ − 20 k ^ Now, on comparing both side, z − 4 y = 14 , 4 x − 5