Suppose $v_1,...,v_n \in V$ are nonzero, mutually orthogonal elements of an inner product space V. Then $v_1,...,v_n$ form an orthogonal basis for their span W = $span(v_1,...,v_n )\subset V$, which is therefore a subspace of dimension n = dimW. In particular, if dimV = n, then $v_1,...,v_n$ form a orthogonal basis for V.
How will I be able to prove this theorem?