Given the points $A ( 0,0,1 ) , B ( 1,1,0 ) , C ( 1,0 , - 1 ) , D ( 1,1,2 )$, it is requested: a) ( 0.75 points) Verify that the points $A , B , C$ and $D$ are not coplanar and find the volume of the tetrahedron they form. b) ( 0.75 points) Find the area of the triangle formed by the points $B , C$ and $D$ and the angle $\hat { B }$ of the same. c) (1 point) Find one of the points $E$ in the plane determined by $A , B$ and $C$ such that the quadrilateral $A B C E$ is a parallelogram. Find the area of said parallelogram.
Given the points $A ( 0,0,1 ) , B ( 1,1,0 ) , C ( 1,0 , - 1 ) , D ( 1,1,2 )$, it is requested:
a) ( 0.75 points) Verify that the points $A , B , C$ and $D$ are not coplanar and find the volume of the tetrahedron they form.
b) ( 0.75 points) Find the area of the triangle formed by the points $B , C$ and $D$ and the angle $\hat { B }$ of the same.
c) (1 point) Find one of the points $E$ in the plane determined by $A , B$ and $C$ such that the quadrilateral $A B C E$ is a parallelogram. Find the area of said parallelogram.