If a vector $\displaystyle v$ is orthogonal to orthonormal basis of a vector space $\displaystyle W$ then why is that $\displaystyle v$ is orthogonal to every vector in $\displaystyle W$?

Is there any theory for this? Is this true? I can't remember any proof of this in my Linear Algebra book.(maybe I forgot)

Can anyone kindly help me figure out the proof of this?