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Question -

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.



Answer -

Given:

Points are (5, 0, 2) and (3, -2, 5)

We need to find the lengths of the edges of the parallelepipedformed

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 isyz-plane

Plane parallel to coordinate planes of y1 and y2 isxz-plane

Plane parallel to coordinate planes of z1 and z2 isxy-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

The edgesof parallelepiped is 2, 2, 3

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