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For the following exercises, find the work done.

Find the work done by vector field $\mathbf{F}(x, y, z)=x \mathbf{i}+3 x y \mathbf{j}-(x+z) \mathbf{k}$ on a particle moving along a line segment that goes from $(1,4,2)$ to $(0,5,1) .$

8 work unit

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Okay, so we're giving the, uh the field f we're just equals two x three x y naked Max. Want to see? We're looking for the work Done from 0 to 1. So bye. The fury of the work theory We have, um f comes the are over dt. So the derogative of replacements The displacements operator thes placements times the operator dt Ah, Plug it in. We have 0 to 1. So the first, um, components will be one minus t. And 2nd 1 will be netting three times t squared among the three t plus four and to t minus three in the Vetter for the directive of the our of our will be making 11 That one. And did he? And this is a who's in the product before into better. So plug everything in. We have necking 30 square, minus 20 plus 14 dc And the answer is eight

University of Illinois at Urbana-Champaign