In this paper we study a class of quadratic differential systems in \(\mathbb {R}^3\) . More precisely, for three distinct families of parameter sets, such differential systems exhibit the property of having an invariant plane. The first family exhibits a first integral in the form of \(H(x,y)= a x + b y\) ensures the invariance of every plane \(a x+b y= \text {constant}\) . Consequently, we describe the phase portraits of the system on each of such planes in the Poincaré disc. The second family has a Darboux invariant of the form \(I(x,y,t)=\left( d_0+ d_1 x+d_2 y\right) e^{-k_0 t}\) which will allow us to describe the phase portraits on the Poincaré ball. Unlike the first two families, the third family lacks both a first integral and a Darboux invariant. Nevertheless, we present a detailed analysis of the phase portraits of these systems on the invariant plane using the Poincaré disc.
