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A vector-valued function of a curve is given by r(t)=−3sinti+3costj+7tk for 0≤t≤2π, (i) Determine the exact value of
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A vector-valued function of a curve is given by r(t)=−3sinti+3costj+7tk for 0≤t≤2π, (i) Determine the exact value of
A vector-valued function of a curve is given by r(t)=−3sinti+3costj+7tk for 0≤t≤2π, (i) Determine the exact value of radius for r(t). [7 marks] (ii) Find dtd[r(t)∙r′(t)]. [2 marks] (iii) Using the formula B(t)=T(t)×N(t), find the binomial vector B(t) to the curve r(t). Give your answer in surd form. [7 marks] b. A particle moves through a 3 -space in such a way that its acceleration is given by a(t)=e−ti+32e−2tj+(t+1)21k. (i) Find the particle's velocity vector given the initial velocity at t=0 is v(0)=i. [5 marks] (ii) Calculate the particle's speed after a very long period of time.
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