Question

A rectangular parallelopiped is formed by drawing planes through the point $(-1,2,5)$ and $(1,-1,-1)$ and parallel to the coordinates planes. The length of the diagonal of the parallelopiped is

Answer 1

The planes forming the parallelopiped are $x=-1,x=1;y=2,y=-1$ and $z=5,z=-1$

Hence, the length of the edges of the parallelopiped are

$1-(-1)=2,|-1-2|=3$ and $|-1-5|=6$

(Length of an edge of a rectangular parallelopiped is the distance between the parallel planes perpendicular to the edge)

$\therefore$ Length of diagonal of the parallelopiped

$=\sqrt{2^2+3^2+6^2}=\sqrt{49}=7$