Given the points $\mathrm { A } ( 1,1,1 ) , \mathrm { B } ( 1,3 , - 3 )$ and $\mathrm { C } ( - 3 , - 1,1 )$, it is requested: a) (1 point) Determine the equation of the plane containing the three points. b) ( 0.5 points) Obtain a point D (different from $\mathrm { A } , \mathrm { B }$ and C ) such that the vectors $\overrightarrow { A B } , \overrightarrow { A C } , \overrightarrow { A D }$ are linearly dependent. c) (1 point) Find a point P on the OX axis, such that the volume of the tetrahedron with vertices A, B, C and P equals 1.
Given the points $\mathrm { A } ( 1,1,1 ) , \mathrm { B } ( 1,3 , - 3 )$ and $\mathrm { C } ( - 3 , - 1,1 )$, it is requested:
a) (1 point) Determine the equation of the plane containing the three points.
b) ( 0.5 points) Obtain a point D (different from $\mathrm { A } , \mathrm { B }$ and C ) such that the vectors $\overrightarrow { A B } , \overrightarrow { A C } , \overrightarrow { A D }$ are linearly dependent.
c) (1 point) Find a point P on the OX axis, such that the volume of the tetrahedron with vertices A, B, C and P equals 1.