Chapter 3, Problem 61P

(a) In unit-vector notation, what is $\stackrel{\to }{r}$ = $\stackrel{\to }{a}$− $\stackrel{\to }{b}$+ $\stackrel{\to }{c}$ if $\stackrel{\to }{a}$ = 5.0 $\hat{i}$ + 4.0 $\hat{j}$ − 6.0 $\hat{k}$, $\stackrel{\to }{b}$ = −2.0 $\hat{i}$ + 2.0 $\hat{j}$ + 3.0 $\hat{k}$, and $\stackrel{\to }{c}$ = 4.0 $\hat{i}$ + 3.0 $\hat{j}$ + 2.0 $\hat{k}$? (b) Calculate the angle between $\stackrel{\to }{r}$ and the positive z axis. (c) What is the component of $\stackrel{\to }{a}$ along the direction of $\stackrel{\to }{b}$? (d) What is the component of $\stackrel{\to }{a}$ perpendicular to the direction of $\stackrel{\to }{b}$ but in the plane of $\stackrel{\to }{a}$ and $\stackrel{\to }{b}$? (Hint: For (c), see Eq. 3-20 and Fig. 3-18; for (d), see Eq. 3-24.)