Vector \(\overrightarrow{\boldsymbol{A}}\) is 2.80 cm long and is \(60.0^{\circ}\) above the \(x\)-axis in the first quadrant. Vector \(\overrightarrow{\boldsymbol{B}}\) is 1.90 cm long and is \(60.0^{\circ}\) below the \(x\)-axis in the fourth quadrant (Fig. E1.39). Use components to find the magnitude and direction of (a) \(\overrightarrow{\boldsymbol{A}}+\overrightarrow{\boldsymbol{B}}\) ; (b) \(\overrightarrow{\boldsymbol{A}}-\overrightarrow{\boldsymbol{B}}\) ; (c) \(\overrightarrow{\boldsymbol{B}}-\overrightarrow{\boldsymbol{A}}\) . In each case, sketch the vector addition or subtraction and show that your numerical answers are in qualitative agreement with your sketch.

Figure E1.39

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,