In this paper, we extend the concepts of norm and numerical radius parallelism by replacing scalar operators with unitary operators. We establish results that generalize those for classical parallelism, and explore several properties and characterizations of these new generalized concepts. Additionally, for \(q \in [0,1]\) , we define \(A\) as q-numerical radius parallel to \(B\) if there exists a complex number \(\lambda\) with unit modulus such that \(\begin{aligned} w_q(A + \lambda B) = w_q(A) + w_q(B), \end{aligned}\) where \(w_q\) denotes the \(q\) -numerical radius. Specifically, for \(q = 0\) , \(w_0(A) = d(A)\) , where \(d(A)\) represents the distance of \(A\) from scalar operators. We also introduce the concepts of scalar distance parallelism and Berezin parallelism, and present results analogous to those established for numerical radius parallelism.
