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(x) =45.6•cos51.2 = 28.57
A(y) = 45.6•sin51.2 =35.74
B(x)= -23.6•cos32.8 = -19.84
B(y) = 23.6•sin32.8=12.78
C(x) = 0
C(y) = -34
(A-B+C)(x)= 28.57-(-19.84) +0 =47.84
(A-B+C)(y) = 35.74-12.78 +(-34)=-11.04
(A-B+C) =sqrt[47.84²+(-11.04)²] = 49.1
tan α= |(A-B+C)(y)|/ (A-B+C)(x)=11.04/47.84=0.23
α =13⁰ (above the +x axis)