Explanation

(c)
$Here,\ force\ \overrightarrow{\mathbf{F}} = 6 \times \frac{(9\widehat{\dot{\mathbf{i}}} + 6\widehat{\dot{\mathbf{j}}} + 2\widehat{\mathbf{k}})}{\sqrt{81 + 36 + 4}}$
$= \frac{6(9\widehat{\dot{\mathbf{i}}} + 6\widehat{\dot{\mathbf{j}}} + 2\widehat{\mathbf{k}})}{11}$
Displacement vector $\overrightarrow{\mathbf{d}}$
$= (7 - 3)\widehat{\dot{\mathbf{i}}} + ( - 6 - 4)\widehat{\dot{\mathbf{j}}} + (8 + 15)\widehat{\mathbf{k}}$
$= 4\widehat{\dot{\mathbf{i}}} - 10\widehat{\dot{\mathbf{j}}} + 23\widehat{\mathbf{k}}$
$\therefore$Work done $= \overrightarrow{\mathbf{F}} \bullet \overrightarrow{\mathbf{d}}$
$= \frac{6}{16}\left( 9\widehat{\dot{\mathbf{i}}} + 6\widehat{\dot{\mathbf{j}}} + 2\widehat{\mathbf{k}} \right) \bullet \left( 4\widehat{\dot{\mathbf{i}}} - 10\widehat{\dot{\mathbf{j}}} + 23\widehat{\mathbf{k}} \right)$
$= \frac{6}{11}(36 - 60 + 46) = 12$