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Question 1304a
Vectors II: Lines and Planes
Equation of a Plane from the Normal Vector
Question
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The planes
p
1
{p_1}
p
1
and
p
2
{p_2}
p
2
are given by
p
1
:
r
⋅
(
−
1
1
0
)
=
−
5
,
p
2
:
r
⋅
(
1
0
0
)
=
1.
\begin{align*} &p_1: \mathbf{r} \cdot \begin{pmatrix} - 1 \\ 1 \\ 0 \end{pmatrix} = - 5,\\ &p_2: \mathbf{r} \cdot \begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix} = 1. \end{align*}
p
1
:
r
⋅
−
1
1
0
=
−
5
,
p
2
:
r
⋅
1
0
0
=
1.
Find the acute angle,
θ
,
{\theta,}
θ
,
between the two planes.
Attempt
θ
=
{\theta = }
θ
=
∘
{^\circ}
∘
Answer
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