Graphics Reference
In-Depth Information
8.3 The normal vector to a planar curve
Given a curve in R
2
of the form y
=
f x, we can construct a tangent vector as shown in
Fig. 8.2, where
dy
dx
j
t
=
i
+
(8.4)
Y
y
=
f
(
x
)
t
n
dy
dx
j
i
X
Figure 8.2.
However, in Section 2.10 we discovered that given a vector
v
=
a
i
+
b
j
then
v
⊥
=−
b
i
+
a
j
Therefore, using Eq. (8.4), we have
dy
dx
i
t
⊥
=−
n
=
+
j
For example, given a function
=
2x
2
+
−
y
3x
4
dy
dx
=
4x
+
3
Therefore,
n
=−
4x
+
3
i
+
j
and when x
=
0,
n
=−
3
i
+
j
