A parallelopiped is formed by planes drawn through the point (2, … - Vidyadip

MCQ

A parallelopiped is formed by planes drawn through the point $(2, 3, 5)$ and $(5, 9, 7)$ parallel to the coordinate planes. The length of a diagonal of the parallelopiped is:

✓
$7$
B
$\sqrt{38}$
C
$\sqrt{155}$
D
none of these

✓

Answer

Correct option: A.

$7$

The given point $(2, 3, 5)$ and $(5, 9, 7)$ are two diagonally opposite vertices of the parallelopiped as all of theire coordinates are different.
$\therefore$ Edges of the paralleloppiped
$= |2 - 5|, |3 - 9|$ and $|5 - 7|$
$=3, 6$ and $2.$
Now,
Length of the diagonal of the parallelopiped
$=\sqrt{3^2+6^2+2^2}$
$=\sqrt{9+36+4}$
$=\sqrt{49}$
$=7$
Hence, length of the diagonal of the parallelepiped formed by the planes
Parallel to coordinate planes and drawn through point $(2, 3, 5)$ and $(5, 9, 7)$ is $7$ units.

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