In Exercises 1 and 2, compute the area of the triangle with the given vertices using both methods.
1. A = (1, - 1), B = (2, 2), C = (4, 0)
2. A = (3, - 1, 4), B = (4, -2, 6), C = (5, 0, 2)
Figure 1 .39 suggests two ways in which vectors may be used to compute the area of a triangle. The area A of

the triangle in part (a) is given by 1/2 ||u|| ||v - proju (v)||, and part (b) suggests the trigonometric form of the area of a triangle: A = 1/2 ||u|| ||v|| sin θ (We can use the identity sin θ = ˆš1 - cos2 θ to find sin θ.)

Transcribed Image Text:

y-proju(v)