Question

Calculus III question on motion in three-space.
How do you solve this problem,
Let r(t)=. Find T(t) and N(t) and show that the decomposition of a(t) is a(t)=(2t/sqrt(t^2+4))T+(4/(t^2+4)N

Answer 1

r""(t) =<2,0>
if you do \[\sqrt{T^2 + N^2}\] you get 2
so that checks out
(at least i think this ishowit works)

T(t) is what unit tangent vector? so just take deriative of r(t) and divie it by norm of it
N(t) is unitnormal right? so take T'over normTalternative ly find some vector N such tahat r' * n (where * is thedot product) =0forgive my tying, hope this helps!