![W = K[ {\frac{1}{3} - \frac{1}{\sqrt{38} } ]](https://tex.z-dn.net/?f=W%20%3D%20K%5B%20%7B%5Cfrac%7B1%7D%7B3%7D%20-%20%5Cfrac%7B1%7D%7B%5Csqrt%7B38%7D%20%7D%20%20%5D)
<u>Explanation:</u>
The parametric representation of a line segment joining the points (a,b,c) and (l,m,n) is
r(t) = (1-t) . (a,b,c) + t . (l, m, n) where t ∈ |0, 1|
So, the parametric representation of a line segment joining the points (3,0,0) and (3,2,5) is
r(t) = (1 - t) . (3,0,0) + t . (3,2,5) where t ∈ |0, 1|
r(t) = (3(1 - t), 0, 0) + (3t, 2t, 5t) where t ∈ |0, 1|
r(t) = (3, 2t, 5t)
Given:

dr = (0, 2, 5) dt


Substitute = 9 + 29t² = u, 92tdt = du
Limit changes from 0→1 to 9 → 38

On solving this, we get:
![W = K[ {\frac{1}{3} - \frac{1}{\sqrt{38} } ]](https://tex.z-dn.net/?f=W%20%3D%20K%5B%20%7B%5Cfrac%7B1%7D%7B3%7D%20-%20%5Cfrac%7B1%7D%7B%5Csqrt%7B38%7D%20%7D%20%20%5D)
Therefore, work done is ![W = K[ {\frac{1}{3} - \frac{1}{\sqrt{38} } ]](https://tex.z-dn.net/?f=W%20%3D%20K%5B%20%7B%5Cfrac%7B1%7D%7B3%7D%20-%20%5Cfrac%7B1%7D%7B%5Csqrt%7B38%7D%20%7D%20%20%5D)