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# Quiz3 - Name MTH 234 Section 60 Answers to Quiz 3 February...

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Name: MTH 234 Section 60 Answers to Quiz 3, February 8 2011 The velocity vector of a curve is given by v ( t ) = t 2 i + (2 t + 1) j + (2 t + t 3 ) k and the curve is at the point (1 , 0 , 1) when t = 0. 1. (2 points) Find the unit tangent vector to the curve when t = 1. Answer: T (1) = v (1) | v (1) | = < 1 , 3 , 3 > 19 2. (2 points) Find the acceleration vector. Answer: a ( t ) = 2 t i + 2 j + (2 + 3 t 2 ) k 3. (3 points) Find the position vector of the curve when t = 1. Answer: r ( t ) = (1 / 3) t 3 i + ( t 2 + t ) j + ( t 2 + t 4 / 4) k + C C = r (0) = i + k r (1) = (4 / 3) i + 2 j + (9 / 4) k 4. (3 points) Write an integral that gives the arc length of the curve from
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