Ruled surfaces constructed by quaternions

In this paper, we define a quaternionic operator whose scalar part is a real parameter and vector part is a curve in three dimensional real vector space R-3. We prove that quaternion product of this operator and a spherical curve represents a ruled surface in R-3 if the vector part of the quaternionic operator is perpendicular to the position vector of the spherical curve. We express this surface as 2-parameter homothetic motion using the matrix representation of the operator. Furthermore, we define another quaternionic operator and show that each ruled surface in R-3 can be obtained by this operator. Finally, we give the geometric interpretations of these operators with some examples. (C) 2020 Elsevier B.V. All rights reserved.