Why line point and plan exist will in fact they are undefined?

Answer 1

They are undefined because they can't be described without using words that are themselves undefined. For example a point has no dimensions. It is a location, or position. But if you describe it that way you have to define location or position. You can't define backwards infinitely, so we accept the meanings of these things as intuitively clear without definitions because they are the building blocks of geometry and are needed to define much more complex terms.