Question

Why the shadow of a plane or a bird doesn't forms?

Answer 1

For a perfect shadow of flying object on the ground from the Sun the size and the distance of the flying objects matters. The objects you mentioned are too small to cast clear shadows form their normal flying height.

At the same time you can see the shadow of the crow or any other birds which is flying 10 ft long from earth surface.

Also keep in mind. What ever flying above the earth surface the speed of the shadow is same as speed of the object.