Thank you for reporting, we will resolve it shortly
Q.
If $\hat{ F }=2 \hat{ i }+\hat{ j }-\hat{ k }$ and $\hat{ r }=3 \hat{ i }+2 \hat{ j }-2 \hat{ k }$, then the scalar and vector products of $\hat{ F }$ and $\hat{ r }$ have the magnitudes respectively as :
$\vec{ F }=2 \hat{ i }+\hat{ j }-\hat{ k } $
$\quad \vec{ r }=3 \hat{ i }+2 \hat{ j }-2 \hat{ k }$
$\vec{ F } \cdot \vec{ r }=6+2+2=10$
$\vec{ F } \times \vec{ r }=\begin{vmatrix}\hat{ i } & \hat{ j } & \hat{ k } \\ 2 & 1 & -1 \\ 3 & 2 & -2\end{vmatrix}$
$=\hat{ i }(0)-\hat{ j }(-1)+\hat{ k }(1)$
$=\hat{ j }+\hat{ k }$
$|\vec{ F } \times \vec{ r }|=\sqrt{2}$