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 :

Question

$\sqrt {{{10} \over 9}} $

$\sqrt {{{5} \over 9}} $

$\sqrt {{{20} \over 9}} $

$\sqrt {{{9} \over 12}} $

Solution

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