Mark the correct statements. i. Every plane curve has a tangent vector different from the zero vector at least in one point. ii. If the tangent vector calculated with the help of parameterization is not a zero vector, then the unit tangent vector of the curve is ±   unequivocal. iii. With the help of derivative parametrization, a normal vector that is not the zero vector can always be formed. iv. A plane curve that does not intersect itself can have at most two different unit normals at each point of the curve. v. If the space curve has one unit normal different from the zero vector at some point, then it has

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.5: Polar Coordinates
Problem 98E
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Mark the correct statements.


i.
Every plane curve has a tangent vector different from the zero vector at least in one point.


ii.
If the tangent vector calculated with the help of parameterization is not a zero vector, then the unit tangent vector of the curve is ±
  unequivocal.


iii.
With the help of derivative parametrization, a normal vector that is not the zero vector can always be formed.

iv.
A plane curve that does not intersect itself can have at most two different unit normals at each point of the curve.


v.
If the space curve has one unit normal different from the zero vector at some point, then it has infinitely many unit normals at this point.

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