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 : $u \times v =\begin{vmatrix} i & j & k \\ 2 & -3 & 1 \\ -3 & 3 & 2 \\ \end{vmatrix}=[(-3)(2)-(1)(3)] i -j [(2)(2) - (1)(-3)]+k [(2)(3) -(-3) (-3)]=- 9i -7j -3k$
Now, the dot product is: $u \cdot (u \times v) =(2i -3j+k)\cdot(- 9i -7j -3k)=[(2)(-9)+(-3)(-7)] +(1)(-3)=-18+21+(-3)=0$
