Answer
$$|\vec{a} \times \vec{b}|=a b$$
Work Step by Step
The vectors can be written as $\vec{a}=a \hat{\mathrm{i}}$ and $\vec{b}=b \hat{\mathrm{j}}$ where $a, b>0$
since $\sin 90^{\circ}=1,$ Eq. $3-24$ gives $|\vec{a} \times \vec{b}|=a b$ where $a$ is the magnitude of $\vec{a}$
$\therefore |\vec{a} \times \vec{b}|=|\vec{b} \times \vec{a}|=a b$
