Planes are drawn through the points (5, 0, 2) and (3, -2, 5) parallel to the coordinate planes. Find the lengths of the edges of the rectangular parallelepiped so formed.
Given: Points are (5, 0, 2) and (3, -2, 5)
To find: lengths of the edges of the parallelepiped formed
For point (5, 0, 2)
x1 = 5, y1 = 0 and z1 = 2
For point (3, -2, 5)
x2 = 3, y2 = -2 and z2 = 5
Plane parallel to coordinate planes of x1 and x2 is yz-plane
Plane parallel to coordinate planes of y1 and y2 is xz-plane
Plane parallel to coordinate planes of z1 and z2 is xy-plane
Distance between planes x1 = 5 and x2 = 3 is 5 – 3 = 2
Distance between planes x1 = 0 and y2 = -2 is 0 – (-2) = 0 + 2 = 2
Distance between planes z1 = 2 and z2 = 5 is 5 – 2 = 3
Hence, edges of parallelepiped is 2, 2, 3