Find a vector perpendicular to the plane that contains the points P(1, 0, 0), Q(2, 0, −1), and R(1, 4, 3).

Question

 (a) Find a vector perpendicular to the plane that contains the points P(1, 0, 0), Q(2, 0, −1),

 and R(1, 4, 3).

(b) Find an equation for the plane that contains P, Q, and R. (Let x, y,

 and z denote the standard coordinate variables.)

(c) Find the area of triangle PQR.

Answer 1

Vector PQ = <1, 0, - 1>; Vector PR = <0, 4, 3>.

Cross product of this vectors gives vector perpendicular vector to this plane:

PQ×PR = det{(i j k} {1, 0, - 1) (0, 4, 3)] = 4i - 3j + 4k