Find the acute angle between the lines with equations r = pmatrix 1 0 4 pmatrix +…

MATHEMATICS · Subjective · CBSE · Mathematics · Three-Dimensional Geometry · Three-Dimensional Geometry

Problem

Find the acute angle between the lines with equations

\mathbf{r} = \begin{pmatrix} 1 \\ 0 \\ 4 \end{pmatrix} + \lambda \begin{pmatrix} 2 \\ 1 \\ -1 \end{pmatrix} \text{ and } \mathbf{r} = \begin{pmatrix} -4 \\ 1 \\ 2 \end{pmatrix} + \mu \begin{pmatrix} 1 \\ 3 \\ -5 \end{pmatrix}.