Question

Equation of the plane passing through the three points $P(2,3,1),Q(2,1,2)$ and $R(3,6,-1)$ is

Answer 1

$P(2,3,1);Q(2,1,2);R(3,6,-1)$

$\Rightarrow \left|\begin{array}{ccc}x-2& y-3& z-1\\ 0& -2& 1\\ 1& 3& -2\end{array}\right|=0$

$\Rightarrow (x-2)\left(1\right)-(y-3)(-1)+(z-1)\left(2\right)=0$

$x-2+y-3+2z-2=0$

$x+y+2z=7$ is the equation of the plane.

Hence, the answer is $x+y+2z=7.$