Chapter 3, Problem 45P

Vectors $\stackrel{\to }{A}$ and $\stackrel{\to }{B}$ lie in an xy plane. $\stackrel{\to }{A}$ has magnitude 8.00 and angle 130°; $\stackrel{\to }{B}$ has components B_x = −7.72 and B_y = −9.20. (a) What is 5 $\stackrel{\to }{A}$· $\stackrel{\to }{B}$? What is 4 $\stackrel{\to }{A}$ × 3 $\stackrel{\to }{B}$ in (b) unit-vector notation and (c) magnitude-angle notation with spherical coordinates (see Fig. 3-34)? (d) What is the angle between the directions of $\stackrel{\to }{A}$ and 4 $\stackrel{\to }{A}$ × 3 $\stackrel{\to }{B}$? (Hint: Think a bit before you resort to a calculation. ) What is $\stackrel{\to }{A}$ + 3.00 $\hat{k}$ in (e) unit-vector notation and (f) magnitude-angle notation with spherical coordinates?

Figure 3-34 Problem 45.