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where
a
1
b
1
c
1
DET
=
a
2
b
2
c
2
a
3
b
3
c
3
Therefore we can state that
d
1
b
1
c
1
d
2
b
2
c
2
d
3
b
3
c
3
x
=
−
DET
a
1
d
1
c
1
a
2
d
2
c
2
a
3
d
3
c
3
y
=
−
DET
a
1
b
1
d
1
a
2
b
2
d
2
a
3
b
3
d
3
z
=
−
DET
If
DET
= 0 two of the planes, at least, are parallel.
Let's test these equations with a simple example. Figure 10.38 shows three
intersecting planes.
The planes shown in Figure 10.38 have the following equations:
x
+
y
+
z
−
2=0
z
=0
y
−
1=0
therefore
111
001
010
DET
=
=
−
1
Y
2
i
+
j
+
k
k
j
P
2
2
Z
X
Fig. 10.38.
Three planes intersecting at point
P
.
