Chapter 2, Problem 2.11CYU

Check Your Understanding For the vectors given in Figure 2.13, find the scalar products $\stackrel{\to }{\text{A}}\cdot \stackrel{\to }{\text{B}}$ and $\stackrel{\to }{\text{F}}\cdot \stackrel{\to }{\text{C}}$ .

The three displacement vectors $\stackrel{\to }{\text{A}}$ , $\stackrel{\to }{\text{B}}$ , and $\stackrel{\to }{\text{C}}$ in Figure 2.13 are specified by their magnitudes $A=10.0,B=7.0$ and $C=8.0$ , respectively, and by their respective direction angles with the horizontal direction $\alpha =35°,\beta =110°$ , and $\gamma =30°$ . The physical units of the magnitudes are centimeters. Choose a convenient scale and use a ruler and a protractor to find the following vector sums: (a) $\stackrel{\to }{\text{R}}=\stackrel{\to }{\text{A}}+\stackrel{\to }{\text{B}}$ , (b) $\stackrel{\to }{\text{D}}=\stackrel{\to }{\text{A}}-\stackrel{\to }{\text{B}}$ , and (c) $\stackrel{\to }{\text{S}}=\stackrel{\to }{\text{A}}-3\stackrel{\to }{\text{B}}+\stackrel{\to }{\text{C}}$ .