Problem $3$:

Two vectors are given in terms of their components by r $=2$i $-3$j $+4$k and F $=20$ i $-10$ k$.$

$1)$ Determine the cross$-$product r x F;

$2)$ Determine the cross$-$product F x r;

$3)$ Calculate the components of the unit vector that is perpendicular to the plane defined by r

and F$.$