Answer:
III quadrant
Explanation:
First of all, let's write the components of each vector along the two directions. We have:
[tex]B_x = B cos 33^\circ = (5.6) cos 33^\circ=-4.7\\B_y = B sin 33^\circ = (5.6) sin 33^\circ=-3.0[/tex]
where we put a negative sign on both components, since they are in the negative x- and y- direction.
Similarly,
[tex]C_x = C sin 22^\circ = (4.8) sin 22^\circ=1.8\\C_y = C cos 22^\circ = (4.8) cos 22^\circ=-4.5[/tex]
where we put a negative sign on the y-direction, since it is along the negative direction.
Now we sum the components along each axis:
[tex]B_x + C_x = -4.7+1.8=-2.9\\B_y + C_y = -3.0 + (-4.5)=-7.5[/tex]
We see that both components of (B+C) are negative, so this vector must be in the 3rd quadrant.
