In order to find the magnitude of the vector sum, proceed as follow:
First, take into account that the vertical and horizontal components of A are (by considering each grid square is 9.00N):
Ax = 3*9.00N = 27.00N
Ay = 4*9.00N = 36.00N
Now, consider that B vector only has a vertical component:
By = -4*9.00N = -36.00N
and the C vector only has a horizontal component:
Cx = -2*9.00N = -18.00N
By and Cx are negative because these component are in the negative part of the y and x axis respectively.
Now, simplify all vertical and horizontal components. It determines the x and y components of the sum vector S:
Sx = Ax+Cx = 27.00N - 18.00N = 9.00N
Sy = Ay+By = 36.00N - 36.00N = 0.00N
Finally, the magnitude of the sum vector is:
[tex]S=\sqrt[]{(S_x)^2+(S_y)^2}=\sqrt[]{(9.00N)^2+(0.00N)^2}=9.00N[/tex]
The magnitude is 9.00N
