Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2012 / Paper 2 / 1 / 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 $bc=3$. ThereforeThe nonzero value of $a$ permits division to find $c$, and the resulting nonzero $c$ determines $b$.