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
Explanation / Answer
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