A parallelopiped is formed by planes drawn through the points $(1,2,3)$ and $(9,8,5)$ parallel to the coordinate planes then which of the following is not the length of an edge of this rectangular parallelopiped
$(A)2\hspace{1cm}(B)4\hspace{1cm}(C)6\hspace{1cm}(D)8$
I see that the numbers $2,8$ appear in the coordintes given.So these can be the edge lengths but $4$ and $6$ are not given in the coordinates.
In my book,$4$ is given to be not the edge length possible.I do not understand why?Why not $6$?Why $6$ can be the possible edge length.Please help me.
Best Answer
A parallelopiped has 6 faces so 3 pairs of parallel planes define a unique parallelopiped.
There will be 3 planes passing through each of these points. For the first point they are $x=1,y=2,z=3$ and for the second one they are $x=9,y=8,z=5$
Taking the distance between pairs of parallel faces we can obtain 3 edge lengths of the parallelopiped as $8,6$ and $2$