Planes are drawn parallel to the coordinates planes through the points (3, 0, -1) and (-2, 5, 4). Find the lengths of the edges of the parallelepiped so formed.
Given: Points are (3, 0, -1) and (-2, 5, 4)
To find: lengths of the edges of the parallelepiped formed
For point (3, 0, -1)
x1 = 3, y1 = 0 and z1 = -1
For point (-2, 5, 4)
x2 = -2, y2 = 5 and z2 = 4
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 = 3 and x2 = -2 is 3 – (-2) = 3 + 2 = 5
Distance between planes x1 = 0 and y2 = 5 is 5 – 0 = 5
Distance between planes z1 = -1 and z2 = 4 is 4 – (-1) = 4 + 1 = 5
Hence, edges of parallelepiped is 5, 5, 5