A vector C = [ 10 m , 30 degree ] and vector D = [ 25 m , 130 degree ]
Use the algebraic ( components) method to find the magnitude and direction of the sum R = C + D ?
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Expert's answer
2011-05-05T10:29:56-0400
The angle between the given vectors is 130-30 = 100 degree. From the Law of cosines the magnitude is R2 = 102 + 252 - 2*10*25*cos (100) = 811.82 m2 R = 28.5 m Using the law of Sinuses we can find the angle between R and C: 28.5/sin100 = 25/sinx , sinx = 0.86, x = 60 degrees. Thus the direction of the vector R is 180-60 + 30 = 150 degree. Answer: 28.5 m, 150 degree.
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