The figure above shows 4 forces 3N, 10N, 3√3N and 6N acting on a particle…

Explanation

Resolution of force:
Total vertical upward force:
= 3√3 + 10 cos 60^o
= 3√3 + 5.
Total downward force
= 6 cos 30^o
= 6 x √(³/₂) = 3√3
Total horizontal forces towards right;
= 3N + cos 30^o
= 3N + 10 x √(³/₂)
= 3N + 5√3
Total horizontal forces towards left:
= 6 cos 60^o
= 6 x 0.5
= 3.0N
Summary:
Vertical resultant forces upward:
= 3√3 + 5 - 3√3
= 5N
Horizontal resultant forces towards right:
= 3N + 5√3 - 3√3
= 5N
Horizontal resultant force towards right
= 3N + 5√3 - 3N
= 5√3N

∴ R² = 5² + (5√3)²
= 25 + 25 x 3
= 100
∴ R = √100
= 10N