Question

Vector A has a magnitude of 6.00 units and is directed at 60° to the positive x-axis. Vector B has a magnitude of 6.00 units and is directed at 120° to the positive x-axis. Find the magnitude and direction of vector C such that A+B+C=0. Place the three vectors so that one begins where the previous ends.What do you observe?

Answer 1

C has a magnitud of 10.4 units and is directed 270° from the positive x-axis

Explanation:

As it shows on the attached picture, the xA and xB have equal magnitudes but opposite directions, therefore they cancel eachother out in the x-axis.

However, the yA and yB are equal in magnitud, but have the same direction. So, the create a total vector the is completely on the y-axis and it's magnitude is 2*(sin(60°)*6)=10.4 units.

In order for C to cancel this vector, it's magnitude also needs to be 10.4 units, but pointing the other way. Therefore, the angle needs to be 270° from the positive x-axis.