$(d)$ $(\hat{ n } \times F ) \times \hat{ n }$

$=-\hat{ n } \times(\hat{ n } \times F )$ $[\therefore A \times B =- B \times A ]$

$=-\{\therefore \hat{n}(\hat{ n } \cdot F )- F (\hat{ n } \cdot \hat{ n })\}$

$\therefore$ Vector triple product is defined as,

$A \times( B \times C ) = B ( A \cdot C )- C ( A \cdot B )$

$= F -\hat{ n }(\hat{ n } \cdot F ) \quad[\therefore \hat{ n } \cdot \hat{ n }=1]$

So, $\quad(\hat{ n } \times F ) \times \hat{ n }= F -\hat{ n }(\hat{ n } \cdot F )$

$\Rightarrow \quad F =\hat{ n }(\hat{ n } \cdot F )+(\hat{ n } \times F ) \times \hat{ n }$

So, $G =(\hat{ n } \times F ) \times \hat{ n }$