How do you find the volume of the parallelepiped with adjacent edges pq, pr, and ps where p(3,0,1), q(-1,2,5), r(5,1,-1) and s(0,4,2)?
The answer is:
Given three vectors, there is a product, called scalar triple product, that gives (the absolute value of it), the volume of the parallelepiped that has the three vectors as dimensions.
The scalar triple product is given by the determinant of the matrix
and the derminant is given for example with the Laplace rule (choosing the first row):
So the volume is: