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Home » 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.
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.
CBSE | Class 11 | Exercise 28.1 | Introduction to Three Dimensional Coordinate Geometry | Maths | RD Sharma
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

    \[\left( 5,\text{ }0,\text{ }2 \right)\text{ }and\text{ }\left( 3,\text{ }-2,\text{ }5 \right)\]

We need to find the lengths of the edges of the parallelepiped formed

For point

    \[\left( 5,\text{ }0,\text{ }2 \right)\]

    \[{{x}_{1}}~=\text{ }5,\text{ }{{y}_{1}}~=\text{ }0\text{ }and\text{ }{{z}_{1}}~=\text{ }2\]

For point

    \[\left( 3,\text{ }-2,\text{ }5 \right)\]

    \[{{x}_{2}}~=\text{ }3,\text{ }{{y}_{2}}~=\text{ }-2\text{ }and\text{ }{{z}_{2}}~=\text{ }5\]

Plane parallel to coordinate planes of

    \[{{x}_{1}}~and\text{ }{{x}_{2}}~is\text{ }yz-plane\]

Plane parallel to coordinate planes of

    \[{{y}_{1}}~and\text{ }{{y}_{2}}~is\text{ }xz-plane\]

Plane parallel to coordinate planes of

    \[{{z}_{1}}~and\text{ }{{z}_{2}}~is\text{ }xy-plane\]

Distance between planes

    \[{{x}_{1}}~=\text{ }5\text{ }and\text{ }{{x}_{2}}~=\text{ }3\text{ }is\text{ }5\text{ }\text{ }3\text{ }=\text{ }2\]

Distance between planes

    \[{{x}_{1}}~=\text{ }0\text{ }and\text{ }{{y}_{2}}~=\text{ }-2\text{ }is\text{ }0\text{ }\text{ }\left( -2 \right)\text{ }=\text{ }0\text{ }+\text{ }2\text{ }=\text{ }2\]

Distance between planes

    \[{{z}_{1}}~=\text{ }2\text{ }and\text{ }{{z}_{2}}~=\text{ }5\text{ }is\text{ }5\text{ }\text{ }2\text{ }=\text{ }3\]

∴Theedges of parallelepiped is

    \[2,\text{ }2,\text{ }3\]

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