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Question 1304c
Vectors II: Lines and Planes
Equation of a Plane from III
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The line
l
{l}
l
and plane
p
{p}
p
are given by
l
:
r
=
(
2
−
2
5
)
+
λ
(
4
0
−
5
)
,
λ
∈
R
,
p
:
r
⋅
(
5
2
4
)
=
−
41.
\begin{align*} &l: \mathbf{r} = \begin{pmatrix} 2 \\ - 2 \\ 5 \end{pmatrix} + \lambda \begin{pmatrix} 4 \\ 0 \\ - 5 \end{pmatrix}, \; \lambda \in \mathbb{R}, \\ &p: \mathbf{r} \cdot \begin{pmatrix} 5 \\ 2 \\ 4 \end{pmatrix} = - 41. \end{align*}
l
:
r
=
2
−
2
5
+
λ
4
0
−
5
,
λ
∈
R
,
p
:
r
⋅
5
2
4
=
−
41.
Find the perpendicular distance between
l
{l}
l
and
p
.
{p.}
p
.
Attempt
Your answer:
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