Answer
(a) The area of the parallelogram spanned by the two vectors $a$ and $b$ is the norm of the cross product of $a$ and $b$. It is also the product of the norms of $a$ and $b$ and the sine of the angle between $a$ and $b$ . That is, $A= |a \times b| = |a| |b| |sin \theta|$; where $\theta$ is the angle between $a$ and $b$.
(b) The volume of the parallelopiped spanned by the three vectors $a$, $b$ and $c$ is the absolute value of the dot product of $a$ and the cross product of $b$ and $c$. That is,
$V=|a. (b \times c)|$
Work Step by Step
(a) The area of the parallelogram spanned by the two vectors $a$ and $b$ is the norm of the cross product of $a$ and $b$. It is also the product of the norms of $a$ and $b$ and the sine of the angle between $a$ and $b$ . That is, $A= |a \times b| = |a| |b| |sin \theta|$; where $\theta$ is the angle between $a$ and $b$.
(b) The volume of the parallelopiped spanned by the three vectors $a$, $b$ and $c$ is the absolute value of the dot product of $a$ and the cross product of $b$ and $c$. That is,
$V=|a. (b \times c)|$
