Question

A rectangular parallelopiped 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 parallelopiped is

• A. $2$
• B. $3$
• C. $6$
• D. $7$

Answer 1

The correct option is D $7$

The plane forming the parallelipiped are

$x=-1,x=1;y=2,y=-1$ and $z=5,z=-1$

Hence, the lengths of the edges of the parallelopiped are

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

$($ length of an edge of the parallelopiped is the distance between the parallel plane sperpendicular to the edge$)$

$\therefore$ Length of diagonal of the parallelopiped

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