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.