Unformatted text preview: (a) A function F ( t ) = ( f ( t ) , g ( t ) , h ( t )) is continuous if and only if each of the functions f, g and h is continuous. (b) If a particle moves in space at constant speed, then it has zero acceleration. (c) The curve parametrized by r ( t ) = (3sin( e t ) , 3cos( e t )) has curvature 1 / 3 at every point. (d) Some plane contains the curve parametrized by F ( t ) = (4cos(3 t ) , 5sin(3 t ) , 6cos(3 t )). 4. (10 points) Suppose a and b are unit vectors and the angle between them is θ . (a) For which θ in [0 , π ] is  a · b  a minimum? (b) For which θ in [0 , π ] is  a · b  a maximum? 5. (10 points) Give a parametrization for the triangle below with the given orientation. [In the original test there was a picture of a speci±c triangle with directions indicated on the edges.]...
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 Spring '08
 Wolfe
 Math, Calculus, Vector Space, Euclidean space, unit tangent vector, standard normal vector

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