Let A → = i ^ + j ^ a n d B → = ( 2 i ^ - j ^ ) . The magnitude of a coplanar vector C → such that A → . C → = B → . C → = A → . B → is given by:

Step-by-step solution

If C → = a i ^   +   b j ^ then, A →   .   C → = A →   .   B →   a + b = 1     . . . . . . . ( i ) B → .   C → =   A →   .   B → 2 a - b = 1     . . . . . . ( ii ) solving equations ( i ) and ( ii ) we get, a = 1 3 ,   b = 2 3 C → =   1 9 + 4 9 =   5 9