  In this article, we generalize the notion of orthogonality as a linear
combination of norm derivatives in order to give a novel concept that we refer
to as $\rho_{\alpha,\beta}$-orthogonality. Also, we discuss some of its
geometric properties in a real normed linear space and present some sufficient
criteria for the smoothness of a normed space by using
$\rho_{\alpha,\beta}$-orthogonality. We provide a few examples to show that the
$\rho_{\alpha,\beta}$- orthogonality cannot be compared to other well-known
orthogonalities in any way. In addition to this, we offer a characterization of
inner product spaces by making use of the functional notation
$\rho_{\alpha,\beta}$. In addition, we show that any
$\rho_{\alpha,\beta}$-orthogonality that preserves linear mapping between two
normed linear spaces must necessarily be a scalar multiple of an isometry.
Also, using the $\rho_{\alpha,\beta}$-functional, we define the idea of an
angle between two vectors and talk about their characteristics in normed
spaces.
