Question

266) (H) Find the resultant of the two vectors. (M1=8.57; A1=58.7) = V1; (M2=3.94; A2=52.1) = V2; (M3,A3)=V3=V1+V2 M=magnitude and A=angle in degrees. answers=M3 and A3 (deg) The resultant of two vectors is the same a the sum of them. There are 2 answers.

Answer 1

Representing vector V1= M1(cosA1+ i sinA1)

=8.57(cos58.7 + i sin58. 7)

= 4.452 + i 7.3222

Similarly writing for vector V2 = 2.420 + i 3.085

Now

V3 = V1+ V2

= 6.872 +i 10.4072

=12.471( cos 56.562 + i sin 56.562)

Hence magnitude of resultant vector = 12.471 = M3

and direction = 56.562 =A3

another possibility is if magnitude , M3 = - 12.471

Then, A3 = 236.562

In that case resultant will be in third quadrant

Thus two possibilities are

1) V3= 12.471( cos 56.562 + i sin56. 562)

2) V3 = - 12.471 (cos236.562 +i sin 236.562)