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Question 1303a
Vectors II: Lines and Planes
Equation of a Plane from the Normal Vector
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The plane
p
{p}
p
is given by
p
:
r
⋅
(
−
1
−
3
1
)
=
6
,
p: \mathbf{r} \cdot \begin{pmatrix} - 1 \\ - 3 \\ 1 \end{pmatrix} = 6,
p
:
r
⋅
−
1
−
3
1
=
6
,
Find the equation of the line
l
{l}
l
that is perpendicular to
p
{p}
p
and contains the point
A
(
5
,
−
3
,
−
4
)
.
{A \left( 5, - 3, - 4 \right).}
A
(
5
,
−
3
,
−
4
)
.
Attempt
l
:
{l: }
l
:
r
=
a
+
λ
d
,
λ
∈
R
.
{\mathbf{r}=\mathbf{a}+\lambda\mathbf{d}, \; \lambda \in \mathbb{R}.}
r
=
a
+
λ
d
,
λ
∈
R
.
a
=
{\mathbf{a}=}
a
=
(
{\Biggl(}
(
)
,
{\Biggr), \quad}
)
,
d
=
{\mathbf{d}=}
d
=
(
{\Biggl(}
(
)
{\Biggr)}
)
Answer
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