Question

Find the length of the diagonal of the parallelepiped formed by planes drawn through the points $(2,3,5)$ and $(5,9,7),$ parallel to the co-ordinate planes?

• A. $\sqrt{38}$ units
• B. $7$ units
• C. $\sqrt{155}$ units
• D. $13$ units

Answer 1

Answer: (B)

$7$ units

Answer 2

Length of the diagonal of he parallelepiped = distance between points $(2,3,5)$ and $(5,9,7)$
$=\sqrt{{{(5-2)}^{2}}+{{(9-3)}^{2}}+{{(7-5)}^{2}}}$
$=\sqrt{{{(3)}^{2}}+{{(6)}^{2}}+{{(2)}^{2}}}$
$=\sqrt{9+36+4}=\sqrt{49}$
$=7\,\,units$