JEE Advance - Mathematics (1994 - No. 13)
The vector $$\,{1 \over 3}\left( {2\widehat i - 2\widehat j + \widehat k} \right)$$ is
a unit vector
makes an angle $${\pi \over 3}$$ with the vector $$\left( {2\widehat i - 4\widehat j + 3\widehat k} \right)$$
parallel to the vector $$\left( { - \widehat i + \widehat j - {1 \over 2}\widehat k} \right)$$
perpendicular to the vector $${3\widehat i + 2\widehat j - 2\widehat k}$$