Answer
$0$
Work Step by Step
Suppose that the two vectors can be represented as: $v=v_1i+v_2j+v_3k$ and $w=w_1i+w_2j+w_3k$, then their cross product of such vectors can be obtained in the form of determinate as :
$ v \times w=\begin{vmatrix} i & j & k \\ v_1 & v_2 & v_3 \\ w_1 & w_2 & w_3 \\ \end{vmatrix}=(v_2w_3-v_3w_2)i-(v_1w_3-v_3w_1)j+(v_1w_2-v_2w_1)k$
Here,we have the cross product of two given vectors as : $u \times v =\begin{vmatrix} i & j & k \\ -3 & 3 & 2 \\ 1 & 1 & 3 \\ \end{vmatrix}=[(3)(3)-(2)(1)] i -j [(-3)(3) - (2)(1)]+k [(-3)(1) -(3) (1)]=7i +11j - 6k$
Now, the dot product is: $u \cdot (u \times v) =(-3+3j+2k)\cdot(7i +11j - 6k)=[(-3)(7)+(3)(11)] +(2)(-6)=-21+33+(-12)=0$
