The magnitude of forces are $40N, 10N$ & $30N$ respectively. Determine the magnitude & direction of their resultant.

This is concurrent system of force system of 3 forces passing through origin

Let F1 be the force in OA

$F1 = F1. rOA \\ = 40[( - i +2j + 4k)/(\sqrt{12+22+42})] \\ = -8.73i + 17.4j + 34.915k N $

Let F2 be the force in OB

$F2 = F2 . rOB \\ = 10[(3i - 3k)/(\sqrt{32+32})] \\ = 7.071i - 7.071k N$

Let F3 be the force in OC

$F3 = F3 . rOC \\ = 30[(2i - 2j + 4k)/(\sqrt{22+22+42})] \\ = 12.247i - 12.247j - 24.5k N$

Now, resultant force

$R = F1 + F2 +F3 \\ R = -10.588 i - 5.153 j - 3.344 k N $

The resultant of force system is $R = -10.588 i - 5.153 j - 3.344 k N $