Perhaps you meant v -> v x u instead of u -> v x u . If so, find first
v x u = ( v_1 , v_2 , v_3 ) x ( -3 , 2 , 3 ) = ...
and apply the reflection to v x u .
The simplest way to find a matrix representation of a linear transformation is to look at what the transformation does to the basis vectors. For example, to map <1, 0, 0> onto <1, 0, 0> X <-3, 2, 3> means to map <1, 0, 0> onto <0, -3, -3>. To map <0, 1, 0> onto <0, 1, 0> X <-3, 2, 3> means to map <0, 1, 0> onto <3, 0, 3>. To map <0, 0, 1> onto <0, 0, 1> X <-3, 2, 3> means to map <0, 0, 1> onto <-2, -3, 0>. The matrix giving that is
[ 0 3 -2]
[ -3 0 -3]
[ -3 3 0]
the matrix having those results as columns. To see that, mutiply that matrix by <1, 0, 0>, <0, 1, 0>, and <0, 0, 1> succesivly.
Reflection in x= z maps <1,0, 0> into <0, 0, 1> and <0, 0, 1> into <1, 0, 0>. Since <0, 1, 0> is in that plane, it is mapped into itself.
The matrix giving that transformation is
[ 0 0 1]
[0 1 0]
[1 0 0]
To find the matrix representing both of those transformations, multiply them (in the proper order, of course).