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Question 1302a
Vectors II: Lines and Planes
Angle 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
=
(
5
−
3
−
1
)
+
λ
(
0
1
5
)
,
λ
∈
R
,
l
2
:
r
=
(
7
2
−
18
)
+
μ
(
1
4
−
1
)
,
μ
∈
R
.
\begin{align*} &l_1: \mathbf{r} = \begin{pmatrix} 5 \\ - 3 \\ - 1 \end{pmatrix} + \lambda \begin{pmatrix} 0 \\ 1 \\ 5 \end{pmatrix}, \; \lambda \in \mathbb{R}, \\ &l_2: \mathbf{r} = \begin{pmatrix} 7 \\ 2 \\ - 18 \end{pmatrix} + \mu \begin{pmatrix} 1 \\ 4 \\ - 1 \end{pmatrix}, \; \mu \in \mathbb{R}. \end{align*}
l
1
:
r
=
5
−
3
−
1
+
λ
0
1
5
,
λ
∈
R
,
l
2
:
r
=
7
2
−
18
+
μ
1
4
−
1
,
μ
∈
R
.
Find the acute angle between the two lines.
Attempt
θ
=
{\theta = }
θ
=
∘
{^\circ}
∘
Answer
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