# Compute Parabolic coordinates-related properties Parabolic coordinates form an orthogonal system, which simplifies the representation of geometric shapes like parabolas and enables straightforward calculations for vector operators due to their identical scale factors. ### :clapper:the orthogonal grid formed by the intersecting parabolas > The demo provides a visual proof that the two families of parabolas always intersect at a right angle. It also shows that the position vector is a direct line from the origin to any point in space, with its components defined by the coordinate system's conversion formulas. {% embed url="" %} ### :pen\_ballpoint:Mathematical Proof {% embed url="" %}