Abstract
Some applications of the linear algebra to analytic geometry are studied; in particular, the results on systems of linear equations to the study of the reciprocal positions concerning lines, planes and vectors in the space are applied. Some concepts developed in a coordinate system of the plane are extended to the space. The geometric problems are solved from both the synthetic point of view, based on the Euclidean axioms and the analytic point of view, by means of equations. Problems of parallelism and perpendicularity about lines and planes, coplanarity, intersections of planes and lines, bundles of planes are solved having recourse to parametric and ordinary representations, linear combinations and determinants.
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Ventre, A.G.S. (2023). Lines and Planes. In: Calculus and Linear Algebra. Springer, Cham. https://doi.org/10.1007/978-3-031-20549-1_15
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DOI: https://doi.org/10.1007/978-3-031-20549-1_15
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Publisher Name: Springer, Cham
Print ISBN: 978-3-031-20548-4
Online ISBN: 978-3-031-20549-1
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