Answer :
As per the given line segments, the work done by the particle is 78N.
Line segments:
In meth, then bounded by two distinct points on a line is called as line segment.
Given,
Here we have a particle moves along line segments from the origin to the points (1, 0, 0), (1, 4, 1), (0, 4, 1), and back to the origin under the influence of the force field below.
And we need to find the work done.
While we have the function in the given question as,
=> F(x,y,z) = z²i + 3xy j + 4y²k
Here we have consider that, If C is the path the particle follows, then work done is ∫ₓᵃ F dx.
Then according to the question the force F(x,y,z) = z²i + 3xy j + 4y²k and all four points are in the plane is written as,
z = 1/4 y
So, if S is the at surface with boundary C, so that S is the portion of the plane over the rectangle is calculated as,
=> D=[0,2] x [0,4].
Then as per the stroke's theorem,
=> ∫∫[2z(0) + 3z(1/4) + 4y]
=> ∫∫3z/4 + 4y
=> [39]₀²
=> 78
To know more about Line segments here.
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