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Question 1303c
Vectors II: Lines and Planes
Equation of a Plane from III
Question
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The line
l
{l}
l
is given by
l
:
r
=
(
−
5
1
1
)
+
λ
(
−
2
3
−
1
)
,
λ
∈
R
.
l: \mathbf{r} = \begin{pmatrix} - 5 \\ 1 \\ 1 \end{pmatrix} + \lambda \begin{pmatrix} - 2 \\ 3 \\ - 1 \end{pmatrix}, \; \lambda \in \mathbb{R}.
l
:
r
=
−
5
1
1
+
λ
−
2
3
−
1
,
λ
∈
R
.
Find the equation of the plane
p
{p}
p
containing both
l
{l}
l
and the point
A
(
−
5
,
0
,
−
5
)
.
{A \left( - 5, 0, - 5 \right).}
A
(
−
5
,
0
,
−
5
)
.
Attempt
p
:
{p: }
p
:
r
⋅
{\mathbf{r}\cdot}
r
⋅
(
{\Biggl(}
(
)
{\Biggr)}
)
=
{=}
=
Answer
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