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Space/Plane equation/Example for intersection/2/Exercise
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We consider the two sets
E
=
{
(
x
y
z
)
∈
R
3
∣
−
3
x
+
2
y
−
6
z
=
0
}
{\displaystyle {}E={\left\{{\begin{pmatrix}x\\y\\z\end{pmatrix}}\in \mathbb {R} ^{3}\mid -3x+2y-6z=0\right\}}\,}
and
F
=
{
(
x
y
z
)
∈
R
3
∣
7
x
−
5
y
−
4
z
=
0
}
.
{\displaystyle {}F={\left\{{\begin{pmatrix}x\\y\\z\end{pmatrix}}\in \mathbb {R} ^{3}\mid 7x-5y-4z=0\right\}}\,.}
Find a description of the intersection
G
:=
E
∩
F
=
{
(
x
y
z
)
∈
R
3
∣
−
3
x
+
2
y
−
6
z
=
0
and
7
x
−
5
y
−
4
z
=
0
}
,
{\displaystyle {}G:=E\cap F={\left\{{\begin{pmatrix}x\\y\\z\end{pmatrix}}\in \mathbb {R} ^{3}\mid -3x+2y-6z=0{\text{ and }}7x-5y-4z=0\right\}}\,,}
similar to
example
.
Create a solution
