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Unformatted text preview: 13.1 Vector Functions and Space Curves We have studied functions, ( ) x f t = , that represent the position of a particle on a line. This notion can be extended to more than 1 dimension. Two functions are required to describe the position of a particle in two dimensions. In three dimensions, 3 functions are required. Consider the following two-dimensional vector function: 2cos ,sin 2 t t t π = ≤ ≤ r . The x component of r is 2cos( ) t and the y component of r is sin( ) t . Hence, we can also describe the vector function by writing ( ) 2cos ( ) sin . x t t and y t t = = For each ( 29 , t t r corresponds to a point in the xy plane. You can graph ( ) t r by plotting these points for 2 t π ≤ ≤ by using the parametric plot function on your calculator. The vector is from the origin to a point on the curve....
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- Fall '08
- vector functions, lim r