Hello, SyNtHeSiS!
The faces of a rectangular box are parallel to the coordinate planes.
Two of the vertices are at the points (1,2,3) and (7,5,4).
Draw the box and label the vertices.
Don't try to make a sketch now . . . wait until the end.
The two points are diametrically opposite vertices.
. . Since goes from 1 to 6, the length of the box is 5.
. . Since goes from 2 to 5, the width of the box is 3.
. . Since goes from 3 to 4, the height of the box is 1.
Consider the "bottom" of the box.
All four vertices of this rectangle have
Plot the points on a twodimensional graph.
Code:

(1,5,3) 6 (7,5,3)
 * → → → → → → → → → → → *
 ↑ ↑
 ↑ ↑
 3↑ ↑3
 ↑ ↑
 ↑ ↑
 * → → → → → → → → → → → *
(1,2,3) 6 (7,2,3)


  +                  

We start at (1,2,3).
We know the length is 6, so we move right 6 units . . . to (7,2,3).
We know the width is 3, so we move up 3 units . . . to (1,5,3).
And we do both: move right 6 units, up 3 units . . . to (7,5,3).
And we have the coordinates of the bottom of the box:
. .
Since the height of the box is 1, add 1 to the coordinates.
And we have the corordinates of the top of the box:
. .
Now I can draw the box . . . and then label the coordinates.
Code:
(1,2,4) (1,5,4)
*      *
/ /
/ / 
/ / *(1,5,3)
/ / /
/ / /
/ / /
/ / /
(7,2,4)*      *(7,5,4)
  /
 /
*      *
(7,2,3) (7,5,3)
And the unseen vertex (in the back) is