Answer :

Given: a parallelepiped is formed by the planes drawn through the points (2, 3, 5) and (5, 9, 7) parallel to the coordinates planes.


To find: length of edges of parallelepiped and length of diagonal


Planes parallel to (2, 3, 5) are:


x = 2, y = 3 and z = 5


Similarly, planes parallel to (5, 9, 7) are:


x = 5, y = 9 and z = 7


Now, let the length of the parallelepiped are L1, L2 and L3


L1 is the length of edge between planes x = 2 and x = 5



Clearly, L1 = 5 – 3 = 2


L2 is the length of an edge between planes y = 3 and y = 9



Clearly, L2 = 9 – 3 = 6


L3 is the length of an edge between planes z = 5 and z = 7



Clearly, L3 = 7 – 5 = 2


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