Determine the magnitude of force F so that the resultant force of the three forces is as small as possible. What is the magnitude of the resultant force?

hello your question is incomplete attached below is the missing diagram

answer : 7.87 KN

Explanation:

The magnitude of the resultant force = 7.87 KN

from fig 1

First step :

calculate the resultant force along the x- direction

Frx = ∑Fx = +8 kN - Fcos45° - 14cos 30°

                = -4.1243 - 0.7071 F

next :

calculate the resultant force along the y- direction

Fry = ∑Fy = -Fsin45° + 14sin30°

                = -0.7071 F + 7

attached below is the remaining part of the  detailed solution