Remarks on the Hardy type inequalities with remainder terms in the framework of equalities

<!-- *** Custom HTML *** --> We study the Hardy type inequalities in the framework of equalities. We present equalities which immediately imply Hardy type inequalities by dropping the remainder term. Simultaneously we give a characterization of the class of functions which makes the remainder term vanish. A point of our observation is to apply an orthogonality properties in general Hilbert space, and which gives a simple and direct understanding of the Hardy type inequalities as well as the nonexistence of nontrivial extremizers.