Aparticle undergoes two displacements. the first has a magnitude of 56.4 cm and makes an angle of 232° with the +x axis. the resultant displacement has a magnitude of 96.3 cm and is directed at an angle of 75.2° to the +x axis. find the magnitude and direction of the second displacement.

There is an easy and convenient technique to solve vectors without drawing them. With you scientific calculator, make sure that you are in mode CMPLX. In this case, the two vectors should sum up to the resultant vector. Since we are given with the resultant vector, let's just use subtraction. Input this into your calculator:

96.3∠75.2° - 56.4∠232°

The answer would be 59.32+137.55i. Convert this to the r∠θ format. The final answer would be 149.8∠66.67°. Therefore, the second displacement is 149.8 cm and makes an angle of 66.67° with the +x axis.

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