Halliday, Resnick & Walker — Vectors: Problem 61

(a) In unit-vector notation, what is \(\vec{r} = \vec{a} - \vec{b} + \vec{c}\) if \(\vec{a} = 5.0\hat{i} + 4.0\hat{j} - 6.0\hat{k}\), \(\vec{b} = -2.0\hat{i} + 2.0\hat{j} + 3.0\hat{k}\), and \(\vec{c} = 4.0\hat{i} + 3.0\hat{j} + 2.0\hat{k}\)? (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. 3.3.1 and Fig. 3.3.1; for (d), see Eq. 3.3.5.)