An application of vector fields is when the vectors represent force Let F ( x , y , z ) be a force field We say that the work done by the force field F ( x , y , z ) over the curve C is given by the equation Work CF ( r ) dr where r ( t ) is some parameterization of C Let F ( x , y , z ) be given by the function F ( x , y , z ) ( x y 2 ) i ( y z 2 ) j ( z x 2 ) k Suppose that a particle moves through the force field F ( x , y , z ) along the line segment running from the point ( 1 , 1 , 1 ) to the point ( 1 , 2 , 1 ) Using the parameterization r ( t ) ( 1 t ) ( 1 , 1 , 1 ) t ( 1 , 2 , 1 ) , at what time t will the force field F ( x , y , z ) have done 0 7 5 units of work on the particle Round your answer to 3 decimal places ( Hint You may want to use the FindRoot command in Mathematica in order to solve this problem ) t

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An application of vector fields is when the vectors represent force  Let F ( x , y , z ) be a force field  We say that the work done by the force field F ( x , y , z ) over the curve C is given by the equation Work   CF ( r ) dr where r ( t ) is some parameterization of C   Let F ( x , y , z ) be given by the function F ( x , y , z )   ( x y 2 ) i   ( y z 2 ) j   ( z x 2 ) k   Suppose that a particle moves through the force field F ( x , y , z ) along the line segment running from the point ( 1 , 1 , 1 ) to the point ( 1 , 2 , 1 )   Using the parameterization r ( t )   ( 1 t ) ( 1 , 1 , 1 )   t ( 1 , 2 , 1 ) , at what time t will the force field F ( x , y , z ) have done 0   7 5 units of work on the particle  Round your answer to 3 decimal places  ( Hint  You may want to use the FindRoot command in Mathematica in order to solve this problem ) t

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An application of vector fields is when the vectors represent force. Let F ( x , y , z ) be a force field. We

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