JEE Math Practice Question

Let $$\overrightarrow a = \widehat i + \widehat j + 2\widehat k$$, $$\overrightarrow b = 2\widehat i - 3\widehat j + \widehat k$$ and $$\overrightarrow c = \widehat i - \widehat j + \widehat k$$ be three given vectors. Let $$\overrightarrow v $$ be a vector in the plane of $$\overrightarrow a $$ and $$\overrightarrow b $$ whose projection on $$\overrightarrow c $$ is $${2 \over {\sqrt 3 }}$$. If $$\overrightarrow v \,.\,\widehat j = 7$$, then $$\overrightarrow v \,.\,\left( {\widehat i + \widehat k} \right)$$ is equal to :

1. A.6
2. B.7
3. C.8
4. D.9