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 $${3\widehat i + 2\widehat j - 2\widehat k}$$