Question

Find the volume of the parallelepiped with one vertex at the origin and adjacent vertices at(1,0,−2),(1,2,3), and (7,1,0)

Answer 1

The signed volume is equal to the scalar triple product of the vectors formed by these vertices:

`(1,0,-2)\cdot((1,2,3)*(7,1,0))=(1,0,-2)\cdot(-3,21,-13)=-29`

Then the volume would be 29.