Statement 1: If the points (1,2,2), (2,1,2), | vedclass

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(A) Let the points be $A(1,2,2), B(2,1,2), C(2,2,z)$ and $D(1,1,1)$.Four points are coplanar if the volume of the tetrahedron formed by them is $0$.Th

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Statement $1$ is false,Statement $2$ is true.

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(A) Let the points be $A(1,2,2), B(2,1,2), C(2,2,z)$ and $D(1,1,1)$.Four points are coplanar if the volume of the tetrahedron formed by them is $0$.The volume of the tetrahedron is given by $\frac{1}{6} |(\vec{b}-\vec{a}) \cdot ((\vec{c}-\vec{a}) 	imes (\vec{d}-\vec{a}))| = 0$.Vectors are $\vec{AB} = (1, -1, 0)$,$\vec{AC} = (1, 0, z-2)$,and $\vec{AD} = (0, -1, -1)$.The scalar triple product is $\begin{vmatrix} 1 & -1 & 0 \ 1 & 0 & z-2 \ 0 & -1 & -1 \end{vmatrix} = 1(0 - (-(z-2))) - (-1)(-1 - 0) + 0 = (z-2) - 1 = z-3$.For the points to be coplanar,$z-3 = 0$,so $z=3$.Statement $1$ claims $z=2$,which is false.Statement $2$ is a standard geometric property: if $4$ points are coplanar,they do not form a $3D$ volume,so the volume of the tetrahedron is $0$. This statement is true.Therefore,Statement $1$ is false and Statement $2$ is true.

Statement $1$: If the points $(1,2,2), (2,1,2), (2,2,z)$ 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 $PQRS$ is $0$.

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Statement $1$: If the points $(1,2,2), (2,1,2), (2,2,z)$ 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 $PQRS$ is $0$.