To see a plane in your dream, may be a pun on someone or something that is "plain". Perhaps the plane refers to a new level.

To dream that you use a plane, denotes that your liberality and successful efforts will be highly commended. To see carpenters using their planes, denotes that you will progress smoothly in your undertakings. To dream of seeing planes, denotes congeniality and even success. A love of the real, and not the false, is portended by this dream.