How to find unit tangent, normal and binormal vectors at a given time (worked example)

An example problem involving the TNB framework of an object moving in a helical pattern is analyzed algebraically, numerically (MATLAB) and graphically (Caclplot3d).

Problem Statement:
Imagine a planet is traveling through the universe along the curve parameterized by r(t)=〈3 cos⁡(t), t, 3 sin(t)〉. What are the planet's unit tangent vector T, unit normal vector N, and unit binormal vector B  at time t= 0.