If a parallelepiped is formed by the planes drawn through the points (2, 3, 5) and (5, 9, 7) parallel to the coordinates planes, then write the lengths of edges of the parallelepiped and length of the diagonal.
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