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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
=
(
4
1
−
5
)
+
λ
(
1
0
5
)
,
λ
∈
R
,
p
:
r
⋅
(
5
4
−
1
)
=
27.
\begin{align*} &l: \mathbf{r} = \begin{pmatrix} 4 \\ 1 \\ - 5 \end{pmatrix} + \lambda \begin{pmatrix} 1 \\ 0 \\ 5 \end{pmatrix}, \; \lambda \in \mathbb{R}, \\ &p: \mathbf{r} \cdot \begin{pmatrix} 5 \\ 4 \\ - 1 \end{pmatrix} = 27. \end{align*}
l
:
r
=
4
1
−
5
+
λ
1
0
5
,
λ
∈
R
,
p
:
r
⋅
5
4
−
1
=
27.
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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