Question

Find the equation of the plane passing through the points P1(1, 2, -1), P2(2, 3, 1) and P3(3, -1, 2)

Answer 1

it is about vector can anyone plz help?

Answer 2

Form vectors p1p2 (1,1,2) and p1p3 (2,-3,3) (which are in the plane)

Take the cross ( ie perpendicular to the plane) by cofactor expansion to give the coefficients of the plane equation

\[\left[\begin{matrix}1 & 2 \\ -3 & 3\end{matrix}\right]\]
minus \[\left[\begin{matrix}1 & 2 \\ 2 & 3\end{matrix}\right]\] and
\[\left[\begin{matrix}1 & 1\\ 2 & -3\end{matrix}\right]\]

or 9,1 and 5. Then, using the point p1

9(x-1) + (y-2) - 5(z+1) = 0

or 9x + y -5z = 16 (which is saisfied by your points).