Mathematics · Ch 4 — Determinants and Matrices
Further Use of Determinants
4.3.4
Further Use of Determinants
Further Use of Determinants
Determinants reappear throughout the rest of the course. This chapter previews — without developing — six further applications you'll meet later:
- Finding the volume of a parallelepiped and a tetrahedron by the vector method.
- Stating the condition for the general second-degree equation to represent a pair of straight lines.
- Finding the shortest distance between two skew lines in three-dimensional geometry.
- Testing whether two lines in three-dimensional geometry intersect. …
Misc 4.3.4Six further applications of determinants (previewed, not developed in this chapter)
Worked out. A bullet list previewing where determinants reappear later in the course: (1) volume of a parallelepiped/tetrahedron by the vector method, (2) the condition for ax²+2hxy+by²+2gx+2fy+c=0 to represent a pair of straight lines, (3) shortest distance between two skew lines, (4) testing whether two lines in 3-D space intersect, (5) cross product and scalar triple product of vectors, (6) forming a differential equation by eliminating an arbitrary constant. …