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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
⋅
(
2
−
1
1
)
=
8
,
p: \mathbf{r} \cdot \begin{pmatrix} 2 \\ - 1 \\ 1 \end{pmatrix} = 8,
p
:
r
⋅
2
−
1
1
=
8
,
Find the equation of the line
l
{l}
l
that is perpendicular to
p
{p}
p
and contains the point
A
(
−
2
,
−
4
,
5
)
.
{A \left( - 2, - 4, 5 \right).}
A
(
−
2
,
−
4
,
5
)
.
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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