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If C= [10m, 30°] and D=[25 m, 130°], what is the direction of the sum of these two vectors?

If C= [10m, 30°] and D=[25 m, 130°], what is the direction of the sum of these two vectors?

Grade:12th pass

1 Answers

Harshit Singh
askIITians Faculty 5901 Points
one month ago
Dear Student


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.

Thanks

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