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Question 1304c
Vectors II: Lines and Planes
Equation of a Plane from III
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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
⋅
(
5
0
4
)
=
37
,
p
2
:
r
⋅
(
5
0
4
)
=
−
45.
\begin{align*} &p_1: \mathbf{r} \cdot \begin{pmatrix} 5 \\ 0 \\ 4 \end{pmatrix} = 37, \\ &p_2: \mathbf{r} \cdot \begin{pmatrix} 5 \\ 0 \\ 4 \end{pmatrix} = - 45. \end{align*}
p
1
:
r
⋅
5
0
4
=
37
,
p
2
:
r
⋅
5
0
4
=
−
45.
Find the perpendicular distance between
p
1
{p_1}
p
1
and
p
2
.
{p_2.}
p
2
.
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