70 VectorsAdditional ProblemsP3.51Let θrepresent the angle between the directions of Aand B. SinceAand Bhave the same magnitudes, A, B, and RAB=+form anisosceles triangle in which the angles are 180°−, 2, and 2. Themagnitude of Ris then RA=FHGIKJ22cos. [Hint:apply the law ofcosines to the isosceles triangle and use the fact that BA=.]Again, A, –B, and DAB=−form an isosceles triangle with apexangle . Applying the law of cosines and the identity1222−=FHGIKJcossinafgives the magnitude of Das DA=FHGIKJ22sin.The problem requires that RD=100.Thus, 222002AAcossinθθFHGIKJ=FHGIKJ. This gives tan.20010FHGIKJ=and=°115..A B R /2A D –BFIG. P3.51P3.52Let represent the angle between the directions of Aand B. SinceAand Bhave the same magnitudes, A, B, and
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