Question

I need the fine the magnitude of the vector sum. ( please see photo )

Answer 1

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:

`S=\sqrt[]{(S_x)^2+(S_y)^2}=\sqrt[]{(9.00N)^2+(0.00N)^2}=9.00N`

The magnitude is 9.00N