Vector is 2.80 cm long and is 60.0o above the x -axis in the first quadrant. Vector is 1.90 cm long and is 60.0o below the x -axis in the fourth quadrant (Fig. E1.35). Use components to find the magnitude and direction of (a) (b) In each case, sketch the vector addition or subtraction and show that your numerical answers are in qualitative agreement with your sketch.

Solution 39E Step 1 of 5: A which is 60 from x-axis with magnitude 2.8 cm can be drawn as, 0 Similarly B which is 60 below x-axis with magnitude 1.9 cm can be drawn as, Step 2 of 5: (a) To find R = A + B Using triangle law, by translating the tile of vector B to the head of A, the resultant vector will be R = A + B as shown in the figure below, o Now the angle between vectors is = 60 , Step 3 of 5: To find the magnitude of resultant vector, R = A + B + 2ABcos Using A= 2.8 cm , B=1.9 cm and = 60o R = (2.8) + (1.9) + 2(2.8)(1.9)cos(60 ) R = .84 + 3.61 + 5.32 R = 16.77 R = 4.09 cm