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

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(A) Let the points be $A(1, 2, 2), B(2, 1, 2), C(2, 2, z)$ and $D(1, 1, 1)$.The points are coplanar if the scalar triple product of vectors $\vec{AB},

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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 $D(1, 1, 1)$.The points are coplanar if the scalar triple product of vectors $\vec{AB}, \vec{AC}$ and $\vec{AD}$ is $0$.$\vec{AB} = (2-1, 1-2, 2-2) = (1, -1, 0)$$\vec{AC} = (2-1, 2-2, z-2) = (1, 0, z-2)$$\vec{AD} = (1-1, 1-2, 1-2) = (0, -1, -1)$The condition for coplanarity is $\begin{vmatrix} 1 & -1 & 0 \ 1 & 0 & z-2 \ 0 & -1 & -1 \end{vmatrix} = 0$.Expanding the determinant: $1(0 - (-(z-2))) - (-1)(-1 - 0) + 0 = 0$$1(z-2) - 1 = 0 \Rightarrow z-3 = 0 \Rightarrow z = 3$.Since $z=3 
eq 2$,Statement $1$ is false.Statement $2$ is a standard geometric property: if four points are coplanar,they do not form a tetrahedron of non-zero volume,hence the volume is $0$. Thus,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 $0$.