A small particle moves to position 5 ^ i - 2 ^ j + ^ k from its...

Work done by a constant force is given by $W = Force\left(\overset{\to}{F}\right) \cdot Displacement\left(\overset{\to}{r}\right)$, where, $\overset{\to}{r} = \overset{\to}{r}2 - \overset{\to}{r}1$

Given here, \overset{\to}{{r}_{1}} = 5\overset{^}{i} - 2\overset{^}{j} + \overset{^}{k} and \overset{\to}{r}2 = 2\overset{^}{i} + 3\overset{^}{j} - 4\overset{^}{k}

So, $W = \overset{\to}{F} \cdot \left(\overset{\to}{r}2 - \overset{\to}{r}1\right)$

= ( 5\overset{^}{i} + 2\overset{^}{j} + 7\overset{^}{k} ) \cdot \left[( 5\overset{^}{i} - 2\overset{^}{j} + \overset{^}{k} ) - ( 2\overset{^}{i} + 3\overset{^}{j} - 4\overset{^}{k} )\right]

$⇒ W = 40J$