Question

find the principal unit normal vector N for the curve r(t) r(t)=(4+t)i+(9+ln(cos t))k, -pie/2< t 14 years ago

Answer 1

long question :(

guess we'll all have to work through it... N(t) = T'(t)/[T'(t)] and T(t)= r'(t)/[r'(t)]...

Answer 2

r(t)= (4+t)i + (9ln(cos(t)))k
r'(t)= 1i + 9ln(u)k... u=cos(t) so using the chain rule it becomes -9sin(t)/cos(t)
or= 1i + (-9sin(t)/cos(t))k
[r'(t)] = sqrt(1 + 81tan(t)^2)