Chapter 9, Problem 14RCC

(a)

To determine

To find:The area of the parallelogram.

Explanation of Solution

The area of parallelogram is the length of the cross product $a\times b$ .

The length of the cross product $a\times b$ is given by,

  $\left|a\times b\right|=\left|a\right|\left|b\right|\sin \theta$

Therefore, the area of parallelogram is the length of the cross product $a\times b$ .

(b)

To determine

To find :The volume of the parallelepiped.

Explanation of Solution

The volume of the parallelepiped determined by the vectors $a,b,c$ is the magnitude of their scalar triple product.

The volume mathematically is given as,

  $V=\left|a\cdot \left(b\times c\right)\right|$

Therefore, the volume of the parallelepiped determined by the vectors $a,b,c$ is the magnitude of their scalar triple product.