Zero curvature => straight line proof

[Shaybay92]

How would you prove that if the curvature of a 'curve' in R3 is zero that the line is straight? All I have learned about is the Serret Frenet equations which I thought only apply when the curvature is non-zero? How do you define normals/binormals in this case?

I'm not sure if this is enough... but:

dT/ds = kN = 0 because k=0
this implies that T is constant at all points ,which implies a straight line?

 

[lavinia]

How would you prove that if the curvature of a 'curve' in R3 is zero that the line is straight? All I have learned about is the Serret Frenet equations which I thought only apply when the curvature is non-zero? How do you define normals/binormals in this case?

I'm not sure if this is enough... but:

dT/ds = kN = 0 because k=0
this implies that T is constant at all points ,which implies a straight line?

the curvature is zero only when the second derivative has no normal component. If you parameterize the curve by arc length then the second derivative is zero.