Given the vector evaluate dr/dt and write it in the form where T is the unit tangent

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Given the vector

r = (1 +t)i + tj + 3 tk

evaluate dr/dt and write it in the form

dr dt = f(t) (t)

where T̂ is the unit tangent direction. Calculate dT̂/dt in its simplest form and show that it is perpendicular to T̂.

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