Explain why or why not Determine whether the following statementsare true and give an explanation or counterexample.a. The position, unit tangent, and principal unit normal vectors (r, T, and N) at a point lie in the same plane.b. The vectors T and N at a point depend on the orientation of a curve.c. The curvature at a point depends on the orientation of a curve.d. An object with unit speed ( | v | = 1) on a circle of radius R has an acceleration of a = N/R.e. If the speedometer of a car reads a constant 60 mi/hr, the car is not accelerating.f. A curve in the xy-plane that is concave up at all points has positive torsion.g. A curve with large curvature also has large torsion.
Explain why or why not Determine whether the following statementsare true and give an explanation or counterexample.a. The position, unit tangent, and principal unit normal vectors (r, T, and N) at a point lie in the same plane.b. The vectors T and N at a point depend on the orientation of a curve.c. The curvature at a point depends on the orientation of a curve.d. An object with unit speed ( | v | = 1) on a circle of radius R has an acceleration of a = N/R.e. If the speedometer of a car reads a constant 60 mi/hr, the car is not accelerating.f. A curve in the xy-plane that is concave up at all points has positive torsion.g. A curve with large curvature also has large torsion.
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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Explain why or why not Determine whether the following statements
are true and give an explanation or counterexample.
a. The position, unit tangent, and principal unit normal vectors (r, T, and N) at a point lie in the same plane.
b. The vectors T and N at a point depend on the orientation of a curve.
c. The curvature at a point depends on the orientation of a curve.
d. An object with unit speed ( | v | = 1) on a circle of radius R has an acceleration of a = N/R.
e. If the speedometer of a car reads a constant 60 mi/hr, the car is not accelerating.
f. A curve in the xy-plane that is concave up at all points has positive torsion.
g. A curve with large curvature also has large torsion.
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