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(Solved): Consider the following curve. x=sin(3t),y=cos(3t),z=12t Using the given parametric equations, gi ...
Consider the following curve. x=sin(3t),y=−cos(3t),z=12t Using the given parametric equations, give the corresponding vector equation r(t). r(t)=⟨sin(3t),−cos(3t),12t⟩ Find r′(t) and ∣r′(t)∣. r′(t)∣r′(t)∣=3cos(3t)i+3sin(3t)j+12k=(3cos(3t))2+(3sin(3t))2+144 Find the equation of the normal plane of the given curve at the point (0,1,4π). Now consider the osculating plane of the given curve at the point (0,1,4π). Determine each of the following. T(t)=⟨153sin(3t),153−cos(3t),15312t⟩T′(t)=∣T′(t)∣=N(t)= Find the equation of the osculating plane of the given curve at the point (0,1,4π).