This paper explores the spatial dimension of Fleming's Left Hand Rule (LHR), commonly-used in Physics instruction for determining the direction of force using the left hand's thumb, forefinger and middle finger. A new instrument was developed to gauge students' ability to coordinate their fingers in 3D space (egocentric frame of reference) based on representations of tasks on paper/screen (allocentric frame of reference). The LHR scores from a sample of 530 Grade 10 and 11 students revealed a significant correlation to standard spatial reasoning measures, with a reliability of 0.77. About 90% of the students scored less than 10 points out of 22, highlighting the relevance of the spatial skills required for articulating the LHR. Science students performed significantly better than non-Science students. The manipulation of the LHR was strongly influenced by the degree of angular disparity between the body frame and task-defined frame and the kinaesthetic constraints required to rotate the triad of fingers as a perpendicular frame.