Consider the following curve. x = sin(6t), y = -cos(6t), z = 18t Using the given parametric equations, give the corresponding vector equation r(t). r(t) = Find r'(t) and Ir'(t)\. r'(t) = |r'(t) = Find the equation of the normal plane of the given curve at the point (0, 1, 37). Now consider the osculating plane of the given curve at the point (0, 1, 37). Determine each of the follo T(t) = T'(t) = IT'(t) = N(t) Find the equation of the osculating plane of the given curve at the point (0, 1, 37).

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