Three vectors are specified as A is 5 m at 45o north of east, B is 7 m at 60o east of south, and C is 4 m at 30o west to south. Find the magnitude and direction of their sum.

Answer 1

A = 5m[45o], CCW.
B = 7m[330o], CCW
C = 4m[240o], CCW.

X=5*Cos45 + 7*Cos330 + 4*Cos240 = 7.60 m
Y=5*sin45 + 7*sin330 + 4*sin240=-3.43 m

Tan A = Y/X = -3.43/7.60 = -0.45113
A = -24.28o = 24.28o S of E = 335.7o, CCW.

Resultant = X/CosA = 7.60/Cos335.7 = 8.34m[335.7]