Find the Resultant and Equilibrant Forces of the given vectors below

Question

A = 500 N to the East

B= 450 N to the South

C = 400 N to the West

D= 550 N to the North

E= 400 N 45° South of West

Answer 1

Decompose all vectors that are not cardinal directions

E_x = 400Ncos(-135) = -200sqrt(2) and E_y = 400Nsin(-135) = -200sqrt(2)

Now add all x vectors with E = pos. x and W= neg.x: 500 -400 - 200sqrt(2) = R_x

add all y vectors with N = pos. y and S = neg. y: -450 + 550 = 200sqrt(2) = R_y

|R| = sqrt(R_x² + R_y²)

θ = arctan(R_y/R_x) (+180 if R_x is negative)

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