The direction of their vector sum is - 20⁰.
Resolution of the vectors into x and y components
Vector Q which is 0.321 m long in a 123° direction and Vector S which is 0.876 m long in a -32.1° direction, can be resolved as follows;
x component of the vectors
Vx = 0.321 m cos 123
Vx = -0.175 m
Sx = 0.876 m x cos(-32.1)
Sx = 0.74 m
Sum of x component of the vectors = 0.74 m - 0.175 m = 0.565 m
y component of the vectors
Vy = 0.321 m x sin(123)
Vy = 0.27 m
Sy = 0.876 m sin(-32.1)
Sy = -0.47 m
Sum of y component of the vector = 0.27 m - 0.47 m = -0.2 m
Direction of the vector
θ = arc tan (Y/X)
θ = arc tan (-0.2 / 0.565)
θ = -20⁰
Thus, the direction of their vector sum is - 20⁰.
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