Explain why or why not. Determine whether the following statement are true and g

ID: 2845373 • Letter: E

Question

Explain why or why not.

Determine whether the following statement 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 a 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 ( I v I =1 ) on a circle of radius R has an acceleration of a = N / R

e) If the spedometer 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

a)false,normal point is at 90 degress to tangent vector

b)true

c)true

d) false,it will have a direction also, which is not mentioned

e)false,speed may be constant,but if the direction of motion changes,then direction of velocity changes so acceleration changes

f)true

g)false

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