Solution
![\[\begin{array}{l} \vec{a}=2 \hat{\imath}-3 \hat{\jmath}+4 k \\ \vec{b}=\hat{\imath}+2 \hat{\jmath}-k \\ \vec{c}=3 \hat{\imath}-2 \hat{\jmath}+2 k \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-69fea7eabbf4a7ab656c0f9cf80ab5be_l3.png "Rendered by QuickLaTeX.com")
To find the volume of parallelepiped it is sufficient to find ![[\vec{a} \vec{b} \vec{c}]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b6ac9f1d6f817c8e298d2f68e0e24ef8_l3.png "Rendered by QuickLaTeX.com")
![\[\vec{a} \cdot \vec{b} \times \vec{c}=\left[\begin{array}{llll} \vec{a} & \vec{b} & \vec{c} \end{array}\right]=\begin{array}{ccc} 2 & -3 & 4 \\ & 2 & -10 \\ & 3 & -2 & 2 \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-adeebfedca75c90a4cf09eda7bd6d457_l3.png "Rendered by QuickLaTeX.com")
But volume cannot be negative
Find the volume of the parallelepiped whose edges are represented by the vectors 
Solution
To find the volume of parallelepiped it is sufficient to find
But volume cannot be negative