Linear collections of vectors in space

Abstract

The article “A simple and more accurate representation of points in 4-dimensional space on a plane using vectors” not only examines in detail the system of vectors on the plane, but also indicates the basis for constructing a linear prima of vectors in space based on two data, namely, that this linear prima consists of segments of the generating hyperbolic paraboloid, enclosed between two guides, of which one is the line of initial points, and the other is the line of end points, and the construction itself can be done by decomposing two given vectors into a component along three coordinate axes and constructing linear parallel vectors from the components; three vectors with a common starting point, but parallel to the coordinate axes, no matter what directions we choose for the latter, are the constituent vectors of a linear prima; the end point of the latter is on the line of end points.