JEE Physics Practice Question

Let $$\overrightarrow A $$ = $$\left( {\widehat i + \widehat j} \right)$$ and, $$\overrightarrow B = \left( {2\widehat i - \widehat j} \right).$$ The magnitude of a coplanar vector $$\overrightarrow C $$ such that $$\overrightarrow A .\overrightarrow C = \overrightarrow B .\overrightarrow C = \overrightarrow A .\overrightarrow B ,$$ is given by :

1. A.$$\sqrt {{{10} \over 9}} $$
2. B.$$\sqrt {{{5} \over 9}} $$
3. C.$$\sqrt {{{20} \over 9}} $$
4. D.$$\sqrt {{{9} \over 12}} $$