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 L_{1}, L_{2} and L_{3}

L_{1} is the length of edge between planes x = 2 and x = 5

Clearly, L_{1} = 5 – 3 = 2

L_{2} is the length of an edge between planes y = 3 and y = 9

Clearly, L_{2} = 9 – 3 = 6

L_{3} is the length of an edge between planes z = 5 and z = 7

Clearly, L_{3} = 7 – 5 = 2

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