vector times cross product 
We have vectors $x, y, z$ where $z = x \times y$.

What is $x \cdot z$?
From my intuition, the cross product is perpendicular to both vectors, so dot product should be 0?

As defined $z$ will be perpendicular to both $x$ and $y$ from the definition of cross product and hence $x.z = 0$ since $z$ is perpendicular to both $x$ and $y$ and as dot product of any two perpendicular vectors is zero due to the involvement of $cos(90^{\circ})$ term.
