Are my results correct?
Task:
Determine the coordinates of a point D such that the points A, B, C and D are the vertices of a parallelogram.
a). A(3|-2|4); B(7|2|1); C(4|6|6)
My solution: D(0|2|9)
b). A(8|4|9); B(4|-1|3); C(5|2|8)
My solution: D(9|7|14)
c). A(3|4|-2); B(-3|-4|2); C(0|0|0)
My solution: D(3|4|-2)
Deduction of point D:
Center of diagonal AC: M = (A+C)/2
The point D lies on the straight line B+2*(M-B)
D=B+2*(M-B)=2*M-B=A+C-B
The first two solutions are correct.
The last task is that A+B=C.
A,B,C lie on a straight line.
No parallelogram can be formed here
The theoretical solution would be D=6.8,-4)=2*A, also on the straight line. Your solution could have noticed that A=D