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In-Depth Information
where
a
1
b
1
c
1
DET
=
a
2
b
2
c
2
a
3
b
3
c
3
The line of intersection is then given by
p
=
p
0
+
λ
n
3
If
DET
= 0 the line and plane are parallel.
To illustrate this, let the two intersecting planes be the
xy
-plane and the
xz
-plane, which means that the line of intersection will be the
y
-axis, as shown
in Figure 10.36.
The plane equations are
z
=0and
x
= 0 therefore
n
1
=
k
n
2
=
i
and
d
1
=0and
d
2
=0
We now compute
n
3
,DET,x
0
,y
0
,z
0
:
ijk
001
100
n
3
=
=
j
001
100
010
DET
=
=1
0
−
0
01
10
00
10
x
0
=
=0
1
0
−
0
00
01
00
10
y
0
=
=0
1
Y
P
n
3
P
0
n
2
n
1
X
Z
Fig. 10.36.
The two intersecting planes create a line of intersection coincident with
the
y
-axis.
