If a parallelepiped is formed by planes drawn through the points (5, 8, 10) and (3, 6, 8) parallel tothe coordinate planes, then the length of diagonal of the parallelepiped is

If a parallelepiped is formed by planes drawn through the points (5, 8, 10) and (3, 6, 8) parallel tothe coordinate planes, then the length of diagonal of the parallelepiped is

A
$2 \sqrt{3}$
B
$3 \sqrt{2}$
C
$\sqrt{2}$
D
$\sqrt{3}$

Solution:

The edge of a parallelepiped = (3 - 5,6 - 8,8 - 10)
= (2, -2, -2)

Length of diagonal

$\begin{matrix} = \sqrt{(- 2)^{2} + (- 2)^{2} + (- 2)^{2}} \\ = \sqrt{4 + 4 + 4} = 2 \sqrt{3} \end{matrix}$

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