First slide

Planes in 3D

Question

A rectangular parallelepiped is formed by drawing planes through the points $(- 1, 2, 5)$ and (1, -1, +1) and parallel to the coordinate planes. The length of the diagonal of the parallelepiped is

Difficult

A

2
B

3
C

6
D

7

Solution

The planes forming the parallelepiped are $x = - 1, x = 1; y = 2, y = - 1$ and $z = 5, = z - 1$
Hence, the lengths of the edges of the parallelepiped are $1 - (- 1) = 2, | - 1 - 2 | = 3$ and $| - 1 - 5 | = 6$ (length of an edge of a rectangular parallelepiped is the distance between the parallel planes perpendicular to the edge)

$∴$ length of diagonal of the parallelepiped = $= \sqrt{2^{2} + 3^{2} + 6^{2}} = \sqrt{49} = 7$

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