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
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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Mark the correct statements.
i.
Every plane curve has a tangent
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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