If a tetrahedron is

defined by three

vectors, the

volume of that tetrahedron can be found by

evaluating the

value of one-sixth of the

scalar triple product. So, if the tetrahedron has

corners at

points A, B, C and D, the three vectors needed are those in the

directions AB, AC and AD. Then the volume V is found by

V = (1/6)(**AD**.**AB**x**AC**).

As an example, let us consider a tetrahedron which is defined by the following vectors:

**AB** = 5**i** - **j** - **k**

**AC** = 2**i** - 8**j** + **k**

**AD** = -**i** + 2**k**

A quick way to evaluate the scalar triple product is to calculate the modulus of the determinant of a matrix consisting of these three vectors:

| / 5 -1 -1 \ |
V = (1/6)| det | 2 -8 1 | |
| \-1 0 2 / |

= (1/6)|5(-16 - 0) + 1(4 + 1) - 1(0 - 8)|

= (1/6)|-80 + 5 + 8|

= (1/6)|-67|

= (1/6)(67)

= 67/6

Therefore the tetrahedron has volume 67/6 units^3.