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Exercise 3.1.6

Avg difficulty 3.0

Consider the following vector equation for a line in R3\mathbb{R}^{3}:

[xyz]=[120]+t [101].\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{r}1\\ 2\\ 0\end{array}\right]+t\,\left[\begin{array}{r}1\\ 0\\ 1\end{array}\right].

Find a new vector equation for the same line by doing the change of parameter t=2−st=2-s.

Selinger, Matrix Theory and Linear Algebra, Lines and planes in Rn, Lines, Exercise 3.1.6

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Adapted from Matrix Theory and Linear Algebra © 2017–2026 Peter Selinger, Lyryx Learning, and Ken Kuttler. Licensed under CC BY 4.0. Source: Matrix Theory and Linear Algebra. Imported at revision d74bc3a.