Question

For p = (1, 2, 1), q = (-1, 3, 2), and r = (1, 1, 1), compute: a. the area of triangle pqr

Answer 1

The area of triangle pqr is sqrt(5)/2.

Step-by-step explanation:

To compute the area of triangle pqr, we can use the formula for the magnitude of the cross product of two vectors. The formula is given by:

|pqr| = 1/2 * |(q - p) x (r - p)|

First, we calculate the vectors (q - p) and (r - p):

(q - p) = (-1 - 1, 3 - 2, 2 - 1) = (-2, 1, 1)

(r - p) = (1 - 1, 1 - 2, 1 - 1) = (0, -1, 0)

Next, we calculate the cross product of (q - p) and (r - p):

(q - p) x (r - p) = (-2, 1, 1) x (0, -1, 0)

= ((1 * 0) - (1 * -1), (-2 * 0) - (1 * 0), (-2 * -1) - (1 * 0))

= (1, 0, 2)

Finally, we calculate the magnitude of the cross product:

|pqr| = 1/2 * |(1, 0, 2)|

= 1/2 * sqrt(1² + 0^2 + 2²)

= 1/2 * sqrt(5)

= sqrt(5)/2