Consider the following vector-valued function:~h(t) =〈2 sin(3t),3 cos(3t),√5 sin(3t)〉0≤t≤2π3This defines a smooth parameterized
curve.(a) Find the unit tangent vector~T(t) for 0≤t≤2π3.(b) Find all of the values oftin the interval 0≤t≤2π3where~h(t) and~T(t) areorthogonal.(c) Show that the curve~h(t) lies on a sphere. What is the radius of the sphere?
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