Question

Show that the four point $(0,-1,-1),(4,5,1)(3,9,4)$ and $(-4,4,4)$ are coplanar

Answer 1

$\begin{array}{c}A(0,-1,-1),B(4,5,1),C(3,9,4),D(-4,4,4)\\ Now,\\ Equationofplanepassesthrough,\\ A,B,Cis\left|\begin{array}{c}xy+1z+1\\ 462\\ 3105\end{array}\right|=0\\ \Rightarrow x(30-20)-(y+1)(20-6)+(z+1)(40-18=0\\ \Rightarrow 10x-14(y+1)+22(z+1)=0\\ SubD(-4,4,4)\\ L.H.S,\\ \Rightarrow 10(-4)-14\left(4\right)+22\left(4\right)+8=0\\ \Rightarrow -40-56+88+8=0\\ \therefore 0=0\\ So,thatA,B,C,Darecoplanner.\\ \end{array}$