Don't worry I found the solution. For those who are interested please follow on.

We have to show that any vector that is orthogonal to orthonormal basis of a subspace is also orthogonal to any vector in that subspace.

Suppose orthonormal basis of is

Also Suppose is a vector and and is orthogonal to each orthonormal basis of subspace so

Let be a vector in so so

as a vector in a space can be written as linear combination of it's basis.

It is necessary to show that

As was to be shown.