2.4 Exercise 6

Given two vectors $\overset{\rightarrow}{A} = − \hat{i} + \hat{j}$ and $\overset{\rightarrow}{B} = 3 \hat{i} - \hat{j}$, find (a) $\overset{\rightarrow}{A} \times \overset{\rightarrow}{B}$, (b) $\left|\overset{\rightarrow}{A} \times \overset{\rightarrow}{B}\right|$, (c) the angle between $\overset{\rightarrow}{A}$ and $\overset{\rightarrow}{B}$, and (d) the angle between $\overset{\rightarrow}{A} \times \overset{\rightarrow}{B}$ and vector $\overset{\rightarrow}{C} = \hat{i} + \hat{k}$.