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Question 1302f
Vectors II: Lines and Planes
Relationship between Lines
Question
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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
=
(
1
−
1
−
5
)
+
λ
(
5
5
−
3
)
,
λ
∈
R
,
l
2
:
r
=
(
3
−
2
−
3
)
+
μ
(
10
10
−
6
)
,
μ
∈
R
.
\begin{align*} &l_1: \mathbf{r} = \begin{pmatrix} 1 \\ - 1 \\ - 5 \end{pmatrix} + \lambda \begin{pmatrix} 5 \\ 5 \\ - 3 \end{pmatrix}, \; \lambda \in \mathbb{R}, \\ &l_2: \mathbf{r} = \begin{pmatrix} 3 \\ - 2 \\ - 3 \end{pmatrix} + \mu \begin{pmatrix} 10 \\ 10 \\ - 6 \end{pmatrix}, \; \mu \in \mathbb{R}. \end{align*}
l
1
:
r
=
1
−
1
−
5
+
λ
5
5
−
3
,
λ
∈
R
,
l
2
:
r
=
3
−
2
−
3
+
μ
10
10
−
6
,
μ
∈
R
.
What is the relationship between the two lines?
Attempt
Select the correct option:
Same
Parallel
Intersecting
Skew
Answer
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