Question 1302f

Vectors II: Lines and Planes
Relationship between Lines

Question

The lines l1{l_1} and l2{l_2} are given by
l1:r=(31−5)+λ(011),  λ∈R,l2:r=(155)+μ(0−12),  μ∈R.\begin{align*} &l_1: \mathbf{r} = \begin{pmatrix} 3 \\ 1 \\ - 5 \end{pmatrix} + \lambda \begin{pmatrix} 0 \\ 1 \\ 1 \end{pmatrix}, \; \lambda \in \mathbb{R}, \\ &l_2: \mathbf{r} = \begin{pmatrix} 1 \\ 5 \\ 5 \end{pmatrix} + \mu \begin{pmatrix} 0 \\ - 1 \\ 2 \end{pmatrix}, \; \mu \in \mathbb{R}. \end{align*}
What is the relationship between the two lines?

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