Question 1302d

Vectors II: Lines and Planes
Perpendicular Distance between Lines

Question

The lines l1{l_1} and l2{l_2} are given by
l1:r=(515)+λ(522),  λR,l2:r=(313)+μ(522),  μR.\begin{align*} &l_1: \mathbf{r} = \begin{pmatrix} 5 \\ 1 \\ 5 \end{pmatrix} + \lambda \begin{pmatrix} - 5 \\ 2 \\ - 2 \end{pmatrix}, \; \lambda \in \mathbb{R}, \\ &l_2: \mathbf{r} = \begin{pmatrix} 3 \\ 1 \\ - 3 \end{pmatrix} + \mu \begin{pmatrix} - 5 \\ 2 \\ - 2 \end{pmatrix}, \; \mu \in \mathbb{R}. \end{align*}
Find the perpendicular distance between the two lines.

Attempt

Your answer:

Answer

Question Progress

  • Start
  • Mastery