(a) In unit-vector notation, what is r = a - b + e if a =

Chapter , Problem 61

(choose chapter or problem)

(a) In unit-vector notation, what is \(\vec{r}=\vec{a}-\vec{b}+\vec{c}\) if \(\vec{a}=5.0 \hat{\mathrm{i}}+4.0 \hat{\mathrm{j}}-6.0 \hat{\mathrm{k}}, \vec{b}=-2.0 \hat{\mathrm{i}}+2.0 \hat{\mathrm{j}}+3.0 \hat{\mathrm{k}}\), and \(\vec{c}=4.0 \hat{\mathrm{i}}+3.0 \hat{\mathrm{j}}+2.0 \hat{\mathrm{k}}\) ?

(b) Calculate the angle between \(\vec{r}\) and the positive z axis.

(c) What is the component of \(\vec{a}\) along the direction of \(\vec{b}\)?

(d) What is the component of \(\vec{a}\) perpendicular to the direction of \(\vec{b}\) but in the plane of \(\vec{a}\) and \(\vec{b}\) ? (Hint: For (c), see Eq. 3-20 and Fig. 3-18; for (d), see Eq. 3-27.)