Question 1196069
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The description is not sufficient to get a single set of answers to the questions that are asked; the specific answers will be different depending on which of the three coordinate axes the points B, D, and E are located.<br>
With A(0,0,0) and G(6,3,2), the other six vertices, in SOME order, are
(6,0,0), (0,3,0), (0,0,2)
(6,3,0), (6,0,2), (0,3,2)<br>
AH, AC, and AF are diagonals of faces of the box; the lengths will again depend on the locations of B, D, and E.<br>
AG is the space diagonal; its length is {{{sqrt(6^2+3^2+2^2)}}}.<br>