Question 1302a

Vectors II: Lines and Planes

Angle between Lines

Question

The lines

{l_1}

and

{l_2}

are given by

\begin{align*} &l_1: \mathbf{r} = \begin{pmatrix} - 3 \\ 1 \\ 5 \end{pmatrix} + \lambda \begin{pmatrix} 4 \\ 3 \\ 1 \end{pmatrix}, \; \lambda \in \mathbb{R}, \\ &l_2: \mathbf{r} = \begin{pmatrix} - 14 \\ - 5 \\ - 9 \end{pmatrix} + \mu \begin{pmatrix} 5 \\ 3 \\ 5 \end{pmatrix}, \; \mu \in \mathbb{R}. \end{align*}

Find the acute angle between the two lines.

{\theta = }

{^\circ}