Represent lines in two- and three-dimensional coordinate geometry using vector, parametric, and symmetric equations, and represent planes in scalar form $ax+by+cz=d$ using normal vectors obtained from coefficients or cross products. Determine intersections by solving linear systems, including the point of intersection or parallel/coincident cases for two-dimensional lines, and intersecting, parallel, coincident, or skew relationships among three-dimensional lines and planes, with plane intersections expressed parametrically when appropriate. Calculate point-to-point, point-to-line, point-to-plane, and parallel-line or parallel-plane distances as minimum Euclidean lengths, identifying zero distance for intersecting objects and common perpendiculars for parallel or skew objects.