Statement 1: If the points $(1,2,2),(2,1,2)$ and $(2,2, z)$ and $(1,1,1)$ are coplanar, then $z=2$.…
Statement 1: If the points $(1,2,2),(2,1,2)$ and $(2,2, z)$ and $(1,1,1)$ are coplanar, then $z=2$.
Statement 2: If the 4 points $P, Q, R$ and $S$ are coplanar, then the volume of the tetrahedron $P Q R S$ is 0.
Statement 1 is false,, Statement 2 is true.
Statement 1 is true, Statement 2 is false.
Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1.
Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.
Solution
Statement-1
Points (1, 2, 2), (2, 1, 2), (2, 2, z) and (1, 1, 1) are coplanar then $z=2$ which is false.
$
\begin{aligned}
& \because\left|\begin{array}{ccc}
1 & -1 & 0 \\
1 & 0 & z-2 \\
0 & -1 & -1
\end{array}\right|=0 \\
& \Rightarrow 1(z-2)+1(-1)=0 \Rightarrow z=3
\end{aligned}
$
Statement $-2$ is the true statement