Slicing vector field in $\mathbb{R}^3$ into vector fields in the plane.

Question

I am trying to draw the vector field $\mathbf{F}_1 = (-y, x, 0)$ in $\mathbb{R}^3$. Seeing that the third component of the field is zero I was wondering whether I could interpret this field as separate layered fields in the $\mathbb{R}^2$ as $\mathbf{F}_2 = (-y, x)$?