Since A is the point (2,1,4) and B is the point (1,4,3), the vector from A to B
is 

< 1-2, 4-1, 3-4 > or < -1, 3, -1 >

Since B is the point (1,4,3) and C is the point (1,0,2), the vector from B to C
is 

< 1-1, 0-4, 2-3 > or < 0, -4, -1 >

Since those vectors are adjacent sides of a parallelogram, the
area of the parallelogram is the magnitude of their cross
product. So we find their cross product:

 = (-3-4)i - (1-0)j + (4-0)k = -7i - j +4k

And the magnitude of their cross product is 


      
(b)

Let D be the point (x1, y1, z1).  Since A is the point (2,1,4),
then the vector from A to D is < x1-2, y1-1, z1-4 >

Since C is the point (1,0,2) and B is the point (1,4,3),

the vector from B to C is < 1-1, 0-4, 2-3 > or < 0, -4, -1 >

Since opposite sides of a parallelogram are equal and parallel,

they must be the same vector.  Therefore we set the corresponding

components  of the vector from A to D,  < x1-2, y1-1, z1-4 > and the vector from B to C < 0,-4,-1 >

equal:

x1-2 = 0, y1-1 = -4, z1-4 = -1,

so

x1=2, y1=-3, z1=3

and the point D is (x1, y1, z1) = (2,-3,3)

Edwin