A particle moves along line segments from the origin to the points (2, 0, 0), (2, 5, 1), (0, 5, 1), and back to the origin under the influence of the force field F(x, y, z) = z2i + 2xyj + 5y2k.

Find the work done.

the work done which is the lie integral = 48

Step-by-step explanation:

From the given question the normal to the plane formed  by the point is estimated as follows:

n = (2,0,0) (0,5,1) = (0,-2,10)

On the plane line, the equation is : -2y + 10z =0

10 z = 2y

Let take an integral look at this function; Vg(x,y,z) = V(-2y+10z) = (0,-2,10)

dS =

By definition; The curl of the vector field is:

Given that F: z² i + 2xy j + 5y² k

Now; by applying stokes theorem, we have :

the work done which is the lie integral = 48

so, converting firstly the mixed fractions to improper fractions and then "adding".

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step-by-step explanation: