JEE Advance - Mathematics (2006 - No. 10)
Let $$\overrightarrow a = \widehat i + 2\widehat j + \widehat k,\,\overrightarrow b = \widehat i - \widehat j + \widehat k$$ and $$\overrightarrow c = \widehat i + \widehat j - \widehat k.$$ A vector in the plane of $$\overrightarrow a $$ and $$\overrightarrow b $$ whose projection on $$\overrightarrow c $$ is $${1 \over {\sqrt 3 }},$$ is
$$4\widehat i - \widehat j + 4\widehat k$$
$$3\widehat i + \widehat j - 3\widehat k$$
$$2\widehat i + \widehat j - 2\widehat k$$
$$4\widehat i + \widehat j - 4\widehat k$$