You are given three vectors. A = 45.6 at θ1 = 51.2° above the +x axis, B = 23.6 at θ2 = 32.8° above the −x axis, and C = 34.0 along the −y axis.
Determine A - B + C (magnitude and angle from the positive x axis).
A = 45.6[51.2o].
B = 23.6[32.8o]
C = 34[270o]
A-B+C = 45.6[51.2o]-23.6[32.8o]+34[270]
X = 45.6*cos51.2-23.6*cos32.8+34*cos270=
8.74.
Y = 45.6*sin51.2-23.6*sin32.8+34*sin270=
-11.2
tanAr = Y/X = -11.2/8.74 = -1.28146
Ar = -52o = Reference angle.
A = -52 + 360 = 308o. = Direction.
Mag. = X/cosA = 8.74/cos308 = 14.2