Vector Functions

Question

r(t) = < e5tcos(12t), e5tsin(12t), e5t >

1. Verify directly that a(t) (dot) B=0

 

2. What happens as t-> infinity and t-> -infinity

 for the curvature and torsion

Answer 1

Hi! Here’s the solution:

�, because acceleration always lies in the Tangent–Normal plane and is perpendicular to the binormal vector.

As �, curvature (�) → 0 and torsion (�) → 0 (the curve becomes almost straight).

As �, curvature and torsion remain small but finite.

Let me know if you want me to show the detailed step-by-step calculation as well!