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Question 1303c
Vectors II: Lines and Planes
Equation of a Plane from III
Question
Generate new
The line
l
{l}
l
and the plane
p
1
{p_1}
p
1
are given by
l
:
r
=
(
5
1
1
)
+
λ
(
−
5
4
−
1
)
,
λ
∈
R
,
p
1
:
r
⋅
(
−
3
−
3
2
)
=
−
16.
\begin{align*} &l: \mathbf{r} = \begin{pmatrix} 5 \\ 1 \\ 1 \end{pmatrix} + \lambda \begin{pmatrix} - 5 \\ 4 \\ - 1 \end{pmatrix}, \; \lambda \in \mathbb{R}, \\ &p_1: \mathbf{r} \cdot \begin{pmatrix} - 3 \\ - 3 \\ 2 \end{pmatrix} = - 16. \end{align*}
l
:
r
=
5
1
1
+
λ
−
5
4
−
1
,
λ
∈
R
,
p
1
:
r
⋅
−
3
−
3
2
=
−
16.
Find the equation of the plane
p
{p}
p
that contains
l
1
{l_1}
l
1
and is perpendicular to
p
1
.
{p_1.}
p
1
.
Attempt
p
:
{p: }
p
:
r
⋅
{\mathbf{r}\cdot}
r
⋅
(
{\Biggl(}
(
)
{\Biggr)}
)
=
{=}
=
Answer
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