Explanation

(b)
Given, force $= 5\left( \frac{2\widehat{\mathbf{i}} - 2\widehat{\mathbf{j}}\mathbf{+}\widehat{\mathbf{k}}}{|2\widehat{\mathbf{i}}\mathbf{- 2}\widehat{\mathbf{j}}\mathbf{+}\widehat{\mathbf{k}}|} \right) = \frac{5}{3}\ (2\widehat{\mathbf{i}}\mathbf{-}2\widehat{\mathbf{j}}\mathbf{+}\widehat{\mathbf{k}}\ )$
Displacement $= \left( 5\widehat{\mathbf{i}} + 3\widehat{\mathbf{j}} + 7\widehat{\mathbf{k}} \right) - (\widehat{\mathbf{i}}\mathbf{+}2\widehat{\mathbf{j}}\mathbf{+}3\widehat{\mathbf{k}})$
$= (4\widehat{\mathbf{i}}\mathbf{+}\widehat{\mathbf{j}}\mathbf{+}4\widehat{\mathbf{k}})$
$\therefore$ Required work done $=$ Force $\bullet$ Displacement
$= \frac{5}{3}\lbrack(2\widehat{\mathbf{i}} - 2\widehat{\mathbf{j}} + \widehat{\mathbf{k}}) \bullet (4\widehat{\mathbf{i}} + \widehat{\mathbf{j}} + 4\widehat{\mathbf{k}})$]
$= \frac{5}{3}\lbrack\ 8 - 2 + 4\rbrack = \frac{50}{3}$ unit