can we say the cutting off their heads and displaying them on the vases or in the vases? would you please give me the reason for using on or in. Thank you looking forward for your assistance.
If part of the surface of the vases is used for the display, it should be "on", but if the interior is used, it should be "in". For instance, if a vase is inverted, with its flat bottom on top, then a severed head balanced on that bottom, the head would be "on" the vase. But if the neck of the head was of a size to fit down in the neck of the upright vase, then the head would be displayed "in" the vase. Similarly, if the severed head was mounted on a pole, and the pole kept upright by having its bottom part stuck down into the vase, then the head would be displayed "in" the vase.
If a depiction of a head is meant, rather than an actual body part, and this image is engraved on the outside of the vase, then that would be "on the vase". Less likely is that the engraving is on the interior of the vase, but if so, that would be "in the vase".
Probably your imagination can supply other physical arrangements for heads and vases, which the general rule about "on" for surfaces and "in" for inside spaces would cover.