  Using density functional theory, we investigate the structure of mixed
$^3$He$_{N_3}$-$^4$He$_{N_4}$ droplets with an embedded impurity (Xe atom or
HCN molecule) which pins a quantized vortex line. We find that the
dopant+vortex+$^4$He$_{N_4}$ complex, which in a previous work [F. Dalfovo {\it
et al.}, Phys. Rev. Lett. {\bf 85}, 1028 (2000)] was found to be energetically
stable below a critical size $N_{\rm cr}$, is robust against the addition of
$^3$He. While $^3$He atoms are distributed along the vortex line and on the
surface of the $^4$He drop, the impurity is mostly coated by $^4$He atoms.
Results for $N_4=500$ and a number of $^3$He atoms ranging from 0 to 100 are
presented, and the binding energy of the dopant to the vortex line is
determined.
