# 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)?

##### 1 Answer

Mar 24, 2015

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.

So:

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: