Given, $$\overrightarrow F = 2\widehat i + \widehat j - \widehat k$$ and $$\overrightarrow r = 3\widehat i + 2\widehat j - 2\widehat k$$

$$\overrightarrow F \,.\,\overrightarrow r = 2(3) + 2(1) + ( - 2)( - 1)$$

$ = 6 + 2 + 2 = 10$

$$\overrightarrow F \times \overrightarrow r = \left| {\begin{matrix} {\widehat i} & {\widehat j} & {\widehat k} \\ 2 & 1 & { - 1} \\ 3 & 2 & { - 2} \\

\end{matrix} } \right|$$

$$ = \widehat i( - 2 + 2) - \widehat j( - 4 + 3) + \widehat k(4 - 3)$$

$$ \Rightarrow \overrightarrow F \times \overrightarrow r = \widehat j + \widehat k$$

$$|\overrightarrow F \times \overrightarrow r | = \sqrt {{1^2} + {1^2}} = \sqrt 2 $$