Step-by-step Solution:

Three forces are: \[ f_1 = 5 \left( \frac{6i + 2j + 3k}{\sqrt{6^2 + 2^2 + 3^2}} \right) = \frac{5}{7} \left( 6i + 2j + 3k \right) \] \[ f_2 = 3 \left( \frac{3i - 2j + 6k}{\sqrt{3^2 + (-2)^2 + 6^2}} \right) = \frac{3}{7} \left( 3i - 2j + 6k \right) \] \[ f_3 = \frac{2i - 3j - 6k}{\sqrt{2^2 + (-3)^2 + (-6)^2}} = \frac{1}{7} \left( 2i - 3j - 6k \right) \] Net force: \[ f = \frac{41i + i + 27k}{7} \] Displacement: \[ \vec d = 3i + 4k \] Work done: \[ f \cdot d = \frac{123 + 108}{7} = 33 \]