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} 4 \\ - 3 \\ 5 \end{pmatrix} + \lambda \begin{pmatrix} 4 \\ 5 \\ 4 \end{pmatrix}, \; \lambda \in \mathbb{R}, \\ &l_2: \mathbf{r} = \begin{pmatrix} 12 \\ - 8 \\ 13 \end{pmatrix} + \mu \begin{pmatrix} 2 \\ - 5 \\ 2 \end{pmatrix}, \; \mu \in \mathbb{R}. \end{align*}

Find the acute angle between the two lines.

{\theta = }

{^\circ}