Solution
= Solution
Expanding the <cross product> gives $\mathbf u\times\mathbf v=(bc,-ac,a)$. Comparing its three components in order from the last to the first gives $a=2$, $ac=6$, and $bc=3$. Therefore
$$
\boxed{a=2,\qquad b=1,\qquad c=3}.
$$
The nonzero value of $a$ permits division to find $c$, and the resulting nonzero $c$ determines $b$.