Exercise 3.1.15

Avg difficulty 3.0

When we computed the angle between two lines in Example 3.18, we calculated two different angles and took the smaller of the two. Show that one can get the same answer by taking the absolute value of the dot product, i.e., by solving

\cos\theta=\frac{\left|\mathbf{u}\boldsymbol{\cdot}\mathbf{v}\right|}{\left\|\mathbf{u}\right\|\left\|\mathbf{v}\right\|}.

Selinger, Matrix Theory and Linear Algebra, Lines and planes in Rn, Lines, Exercise 3.1.15

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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.