Let a → = 2 i ^ + λ 1 j ^ + 3 k ^ , b → = 4 i ^ + 3 - λ 2 j ^ + 6 k ^ and c → = 3 i ^ + 6 j ^ + λ 3 - 1 k ^ be three vectors such that b → = 2 a → and a → is perpendicular to c → . Then a possible value of λ 1 , λ 2 , λ 3 is

Step-by-step solution

Since b → = 2 a → , so 3 - λ 2 = 2 λ 1 λ 2 = 3 - 2 λ 1       . . . 1 We know that if two vectors a 1 i ^ + b 1 j ^ + c 1 k ^ and a 2 i ^ + b 2 j ^ + c 2 k ^ are perpendicular, then a 1 a 2 + b 1 b 2 + c 1 c 2 = 0 Since, a → is perpendicular to c → so 6 + 6 λ 1 + 3 λ 3 - 1 = 0 ⇒ 6 + 6 λ 1 + 3 λ 3 - 3 = 0 ⇒ λ 3 = - 1 - 2 λ 1     . . . 2 From equations 1 and 2 , we get λ 1 ,   λ 2 ,   &#95