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Question 1302b
Vectors II: Lines and Planes
Point of Intersection of Lines
Question
Generate new
The lines
l
1
{l_1}
l
1
and
l
2
{l_2}
l
2
are given by
l
1
:
r
=
(
3
1
3
)
+
λ
(
−
3
4
4
)
,
λ
∈
R
,
l
2
:
r
=
(
0
6
14
)
+
μ
(
1
−
1
1
)
,
μ
∈
R
.
\begin{align*} &l_1: \mathbf{r} = \begin{pmatrix} 3 \\ 1 \\ 3 \end{pmatrix} + \lambda \begin{pmatrix} - 3 \\ 4 \\ 4 \end{pmatrix}, \; \lambda \in \mathbb{R}, \\ &l_2: \mathbf{r} = \begin{pmatrix} 0 \\ 6 \\ 14 \end{pmatrix} + \mu \begin{pmatrix} 1 \\ - 1 \\ 1 \end{pmatrix}, \; \mu \in \mathbb{R}. \end{align*}
l
1
:
r
=
3
1
3
+
λ
−
3
4
4
,
λ
∈
R
,
l
2
:
r
=
0
6
14
+
μ
1
−
1
1
,
μ
∈
R
.
Find the coordinates of the point of intersection between the two lines.
Attempt
Your answer:
(
{\Big(}
(
,
,
)
{\Big)}
)
Answer
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