Chapter 1, Problem 71CCP

The figure shows three displacement vectors  $\stackrel{\to }{A}$ ,  $\stackrel{\to }{B}$ , and  $\stackrel{\to }{C}$ . These vectors are arranged in tail-to-head fashion, and they add together to give a resultant displacement  $\stackrel{\to }{R}$ , which lies along the x axis. Note that the vector  $\stackrel{\to }{B}$  is parallel to the x axis. Concepts: (i) How is the magnitude of  $\stackrel{\to }{A}$  related to its scalar components  $A_x and A_y$ ? (ii) Do any of the vectors in the figure have a zero value for either their x or y components? (If so, which ones?) (iii) What does the fact that  $\stackrel{\to }{A}$ ,  $\stackrel{\to }{B}$ , and  $\stackrel{\to }{C}$  add together to give  $\stackrel{\to }{R}$  tell you about the components of these vectors? Calculations: What is the magnitude of the vector  $\stackrel{\to }{A}$  and its directional angle ??