If a → = i ^ + j ^ + k ^ , b → = i ^ - j ^ + 2 k ^ and c → = x i ^ + x - 2 j ^ - k ^ and if the vector c → lies in the plane of vectors a → and b → , then x equals

Step-by-step solution

Given a → = i ^ + j ^ + k ^ ,   b → = i ^ - j ^ + 2 k ^ and c → = x i ^ + x - 2 j ^ - k ^ . Since, the vector c → lies in the plane of vectors a → and b → , therefore a → ,   b → and c → are coplanar. If three vectors a 1 i ^ + a 2 j ^ + a 3 k ^ ,   b 1 i ^ + b 2 j ^ + b 3 k ^ and c 1 i ^ + c 2 j ^ + c 3 k ^ are coplanar, then a 1 a 2 a 3 b 1 b 2 b 3 c 1 c 2 c 3 = 0 . ∴   1 1 1 1 - 1 2 x x - 2 - 1 = 0 ⇒ 1 × 1 - 2 x + 4 - 1 &#