Page 227 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

Area of a Parallelogram is equal to the area of the parallelogram determined by u and v.
If u and v are vectors in 3-space, then

EXAMPLE 4 Area of a Triangle , , and .
Find the area of the triangle determined by the points

Solution

The area A of the triangle is the area of the parallelogram determined by the vectors and (Figure 3.4.5). Using the
. It follows that
method discussed in Example 2 of Section 3.1, and

and consequently,

Figure 3.4.5

DEFINITION

If u, v, and w are vectors in 3-space, then

is called the scalar triple product of u, v, and w.

The scalar triple product of , , and can be calculated from the formula

(7)

This follows from Formula 4 since