The two vectors and in fig. 3-28 have equal magnitudes of 10.0 m and the angles are 30â° and 105â°. find the (a) x and (b) y components of their vector sum , (c) the magnitude of , and (d) the angle makes with the positive direction of the x axis.

It would help a lot if you use technology to answer this problem. You can easily input the given data to your scientific calculator. Make sure to put it in CMPLX mode. Then, input the two vectors as shown below:

10∠30° + 10∠105°

The answer would be 6.072+14.659i. This is not yet the final answer. Convert this to the r∠θ form. It would turn to 15.87∠67.5°. That means that the magnitude of the resultant vector is 15.87 and it makes an angle of 67.5° with the positive x-axis.