Question 1302b

Vectors II: Lines and Planes

Point of Intersection of Lines

Question

The lines

{l_1}

and

{l_2}

are given by

\begin{align*} &l_1: \mathbf{r} = \begin{pmatrix} 4 \\ 3 \\ 0 \end{pmatrix} + \lambda \begin{pmatrix} - 1 \\ 4 \\ 2 \end{pmatrix}, \; \lambda \in \mathbb{R}, \\ &l_2: \mathbf{r} = \begin{pmatrix} - 6 \\ 4 \\ 8 \end{pmatrix} + \mu \begin{pmatrix} - 4 \\ 3 \\ 4 \end{pmatrix}, \; \mu \in \mathbb{R}. \end{align*}

Find the coordinates of the point of intersection between the two lines.

Your answer:

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