Question

A rectangular parallelopiped is formed by planes drawn through the points (5, 7, 9) and (2, 3, 7) parallel to the coordinate planes. The length of an edge of this rectangular parallelopiped is
(a) 2
(b) 3
(c) 4
(d) all of these

Answer 1

$$\begin{gathered} \left(\mathrm{d}\right)\mathrm{all}\mathrm{of}\mathrm{these} \\ \mathrm{The}\mathrm{given}\mathrm{points}\left(5,7,9\right)\mathrm{and}\left(2,3,7\right)\mathrm{are}\mathrm{two}\mathrm{diagonally}\mathrm{opposite}\mathrm{vertices}\mathrm{of}\mathrm{the}\mathrm{parallelopiped}\mathrm{as}\mathrm{all}\mathrm{of}\mathrm{their}\mathrm{coordinates}\mathrm{are}\mathrm{different}. \\ \therefore \mathrm{Edges}\mathrm{of}\mathrm{the}\mathrm{parallelopiped}=\left|5-2\right|,\left|7-3\right|,\left|9-7\right| \\ =3,4,2 \end{gathered}$$