VECTOR QUESTION

Question

A triangle in space is defined by the points P = (1,1,2), Q = (−1,0,3) and R = (2,1,−1).

 

Find a vector form and the parametric equations for the equation of the line passing
through P and perpendicular to the triangle PQR.

Answer 1

Let u = PQ = <-1-1, 0-1, 3-2> = <-2, -1, 1>

 

Let v = PR = <2-1, 1-1, -1-2> = <1, 0, -3>

 

u x v is perpendicular to the triangle and parallel to the desired line

 

    u x v = <3, -5, 1>

 

Vector form of the line:  <x, y, z> = t<3, -5, 1> + <1, 1, 2>

 

Parametric equations:  x = 3t+1

                                 y = -5t+1

                                 z = t + 2