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Question 1304e
Vectors II: Lines and Planes
Cartesian and Vector Equation of a Plane
Question
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The line
l
{l}
l
and the plane
p
{p}
p
are given by
l
:
r
=
(
2
1
−
2
)
+
λ
(
1
5
1
)
,
λ
∈
R
,
p
:
r
⋅
(
−
1
1
−
4
)
=
8.
\begin{align*} &l: \mathbf{r} = \begin{pmatrix} 2 \\ 1 \\ - 2 \end{pmatrix} + \lambda \begin{pmatrix} 1 \\ 5 \\ 1 \end{pmatrix}, \; \lambda \in \mathbb{R}, \\ &p: \mathbf{r} \cdot \begin{pmatrix} - 1 \\ 1 \\ - 4 \end{pmatrix} = 8. \end{align*}
l
:
r
=
2
1
−
2
+
λ
1
5
1
,
λ
∈
R
,
p
:
r
⋅
−
1
1
−
4
=
8.
What is the relationship between the line and the plane?
Attempt
Select the correct option:
Intersect at exactly one point
Line lies in plane
Line is parallel to (but not in) plane
Answer
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