Find the volume of the parallelepiped whose coterminous edges are represented by the vectors: i,` 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` ii, ` 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` iii, ` vec a=11 hat i , vec b=2 hat j , vec c=13 hat k` iv, ` vec a= hat i+ hat j+ hat k , vec b= hat i- hat j+ hat k , vec c= hat i+2 hat j- hat k`

Explanation

To find the volume of the parallelepiped formed by the vectors, we can use the scalar triple product, which is given by the formula:

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

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

\[
V = \begin{vmatrix}
...