Help me with finding the equation of the Plane containing the points: p=(2,1,3), q=(1,0,1) and r=(2,-1,1).

Question

Given three points p=(2,1,3), q=(1,0,1) and r=(2,-1,1), find the Cartesian equation of the plane containing those points.

Answer 1

Evaluate the direction vectors $\;\vec v:=\vec{pq}=q-p\;,\;\;\vec u=\vec{pr}=r-p\;$, then evaluate the vectorial product $\;(a,b,c)=\vec v\times\vec u\;$ , and this last is a normal vector to your plane, so your plane is $\;ax+by+cz+d=0\;\;$ . Finally, can you see how to evaluate $\;d\;$ ?