The Unit Tangent Vector T
Let r(t) be a differentiable vector valued function and
be the velocity vector. Then we define the unit tangent vector
by as the unit vector in the direction of the velocity vector:
Example:
Find the unit tangent vector of
Solution:
Example:
Find the unit tangent vector of the curve
Solution:
because t>0).
Example:
find T(t) and T(0). Let
Solution:
.
Exercise:
Find the unit tangent vector of
Curvature:
The curvature can be defined as: .
i.e.,
Remark:
The radius of curvature can be denoted as:
Example:
find curvature. If
Solution:
And
Example:
if Find the curvature at
Solution:
And
And
Exercise:
find curvature if
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