Let u and v be vectors in be the angle between u and v. (a) Prove that . [Hint: Use Pr...

Let u and v be vectors in be the angle between u and v.

(a) Prove that . [Hint: Use Problem 6(c).]

(b) Prove that the area A of the triangle determined by u and v (as shown in Figure 1.71) is given by

(c) Use the result in part (b) to compute the area of the triangle with vertices A = (1, 2, 1), B = (2, 1, 0), and C = (5, -1, 3).