Consider the helix X (t) = ( cos( −3 t), sin( −3 t), 1 t ). Compute, at t = [(π)/6]:

A. The unit tangent vector T = ??? I+ ??? J+ ??? K

B. The unit normal vector N = ??? I+ ??? J+ ??? K

Question

Consider the helix X (t) = ( cos( −3 t), sin( −3 t), 1 t ). Compute, at t = [(π)/6]:

A. The unit tangent vector T = ??? I+ ??? J+ ??? K

B. The unit normal vector N = ??? I+ ??? J+ ??? K

anonymous · Answer

remember the T=dT/dt/|dT/dt|
Normal is 1/k(dT/ds)
dT/dt/(ds/dt)=dT/ds
ds/dt=r'(t) or X'(t)  and the k(t) if from the other posts, look up the derivation

WHEN i did these to understand them i made up some which i knew where the N and T would be going along with the k(t)

just practice these with r(t)=(rcos(t),rsin(t),t/6)  looks like a spiral