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Question 1302d
Vectors II: Lines and Planes
Perpendicular Distance between Lines
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The lines
l
1
{l_1}
l
1
and
l
2
{l_2}
l
2
are given by
l
1
:
r
=
(
5
1
5
)
+
λ
(
−
5
2
−
2
)
,
λ
∈
R
,
l
2
:
r
=
(
3
1
−
3
)
+
μ
(
−
5
2
−
2
)
,
μ
∈
R
.
\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*}
l
1
:
r
=
5
1
5
+
λ
−
5
2
−
2
,
λ
∈
R
,
l
2
:
r
=
3
1
−
3
+
μ
−
5
2
−
2
,
μ
∈
R
.
Find the perpendicular distance between the two lines.
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Your answer:
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