Halliday, Resnick & Walker — Vectors: Problem 66

Consider $\vec{a}$ in the positive direction of $x$, $\vec{b}$ in the positive direction of $y$, and a scalar $d$. What is the direction of $\vec{b}/d$ if $d$ is (a) positive and (b) negative? What is the magnitude of (c) $\vec{a} \cdot \vec{b}$ and (d) $\vec{a} \cdot \vec{b}/d$? What is the direction of the vector resulting from (e) $\vec{a} \times \vec{b}$ and (f) $\vec{b} \times \vec{a}$? (g) What is the magnitude of the vector product in (e)? (h) What is the magnitude of the vector product in (f)? What are (i) the magnitude and (j) the direction of $\vec{a} \times \vec{b}/d$ if $d$ is positive?