Volume of a Parallelepiped A parallelepiped is a prism whose faces are all parallelograms. Let A, B, and C be the vectors that define the parallelepiped shown in the figure. The volume V of the parallelepiped is given by the formula

$V=\left|(A\times B).C\right|$

Find the volume of a parallelepiped if the defining vectors are

$$\begin{gathered} \overrightarrow{A}=3\hat{i}-2\hat{j}+4\hat{k} \\ \overrightarrow{B}=2\hat{i}+\hat{j}-2\hat{k} \\ \overrightarrow{C}=3\hat{i}-6\hat{j}-2\hat{k} \end{gathered}$$

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!