Once you have found the vectors then all you need is a way of computing the volume of the parallelepiped spanned by these vectors. I suggest that you take a look at the geometrical relationship between the determinant of a matrix and the shape spanned by its column vectors.
I didn't want to give too much away! You can find the answer in most good books on Linear Algebra, or even the Wikipedia page about determinants.
This assumes, of course, that the hint you were given is true. I don't actually know how to prove that, so if anyone knows I would like to know!