Answer:
57 u^3
Step-by-step explanation:
We know that the volume of the parallelepiped determined by the tree vectors is equal to the absolute value of its scalar triple product:
[tex]V = |(a\times b)\cdot c|=| \det \left( \left[\begin{array}{ccc}1&3&2\\-1&1&5\\4&1&3\end{array}\right] \right)| = |1(3-5) - 3(-3-20)+2(-1-4)| = |-2+69-10|=|57|=57[/tex]
Where we used that the scalar triple product of three vectors equals the absolute value of its determinant.
Therefore, the volume of the parallelepiped is: 57 u^3
