Find the volume of the parallelepiped whose coterminous edges are represented by the vector: ` vec a=2 hat i-3 hat j+4 hat k ,\ vec b= hat i+2 hat j- hat k ,\ vec c=3 hat i- hat j-2 hat k` .

Explanation

To find the volume of the parallelepiped formed by the vectors \(\vec{a}\), \(\vec{b}\), and \(\vec{c}\), we will use the scalar triple product, which is given by the formula:

\[ V = |\vec{a} \cdot (\vec{b} \times \vec{c})| \]

This can also be calculated using the determinant of a matrix formed by the vectors. The volume \(V\) can be expressed as:

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