Three vectors a , b , and c, each have a magnitude of 44 m and lie in an xy plan

Question

Three vectors a , b , and c, each have a magnitude of 44 m and lie in an xy plane. Their directions relative to the positive direction of the x axis are 25 ?, 192 ?, and 314 ?, respectively. What are (a) the magnitude and (b) the angle of the vector a+b+c (relative to the +x direction in the range of (-180,180)) , and (c) the magnitude and (d) the angle of a-b+c in the range of (-180,180)? What are (e) the magnitude and (f) the angle (in the range of (-180,180)) of a fourth vector d such that (a+b) - (c+d) = 0 ?

Please help. I can't figure it out for some reason.

Explanation / Answer

Writing in vector form,
a = 44 cos(25 deg) i^ + 44 sin(25 deg) j^ = 39.878 i^ + 18.595 j^
b = 44 cos(192 deg) i^ + 44 sin(192 deg) j^ = -43.038 i^ - 9.148 j^
c = 44 cos(314 deg)i^ +44sin(314 deg) j^ = 30.565 i^ -31.651 j^
a) a+b+c = 27.405i^ -22.204 j^
magnitude = 35.271
b) angle = -39 deg
c) a-b+c = 113.481 i^ -3.908 j^
magnitude = 113.548
d) angle = -1.972 deg
e) a+b-c-d = 0
d = a+b-c = -33.725 i^ + 41.098 j^
magnitude = 53.164
f) angle = 180-50.628 = 129.37 deg.

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