Graphics Reference
In-Depth Information
x
R
1 z
R
x
S
1 z
S
x
T
1 z
T
z
S
−
z
R
x
S
−
x
R
=
=
b
or b
z
T
−
z
R
x
T
−
x
R
x
R
y
R
1
x
S
y
S
1
x
T
y
T
1
x
S
−
x
R
y
S
−
y
R
c
=
or c
=
x
T
−
x
R
y
T
−
y
R
d
=
ax
R
+
by
R
+
cz
R
4.5 A plane perpendicular to a line and passing through a point
Although there are an infinite number of planes perpendicular to a given line, simply by defining
a point that lies on a plane enables us to fix a unique plane. In this section we derive a formula
that defines the Cartesian form of the plane equation using a line and a point. The line represents
a vector perpendicular to a plane, while the point identifies a specific plane in space.
Y
P
n
p
Q
q
Z
X
Figure 4.5.
With reference to Fig. 4.5, let the plane equation be
ax
+
by
+
cz
=
d
and the line direction vector be
=
+
+
n
a
i
b
j
c
k
and the specified point on the plane be
Q
x
Q
y
Q
z
Q
