Vectors a i ^ + b j ^ + k ^ and 2 i ^ - 3 j ^ + 4 k ^ are perpendicular to each other when 3 a + 2 b = 7 , the ratio of a to b is x 2 . The value of x is _____.

Step-by-step solution

Dot product of two perpendicular vectors will be zero. Therefore, a i ^ + b j ^ + k ^ · 2 i ^ - 3 j ^ + 4 k ^ = 0 ⇒ 2 a - 3 b + 4 = 0       . . . E q ( 1 ) As given in the question, 3 a + 2 b = 7       . . . E q ( 2 ) From both equations, we get a = 1   &   b = 2 Then, a b = x 2 ⇒ x = 2 a b = 2 × 1 2 ⇒     x = 1