Question

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

• A. 7 units
• B. $\sqrt{38}unit$
• C. $\sqrt{155}unit$
• D. none of these

Answer 1

The correct option is A 7 units

The length of a diagonal of the parallelopiped is $\sqrt{a^2+b^2+c^2}$,

Where $a=x_2-x_1,b=y_2-y_1$ and $=z_2-z_1$

A parallelopiped is formed by planes drawn through the points $(2,3,5)$ and $(5,9,7)$ parallel to the coordinates planes.

Let $a,b,c$ be lengths of edges, then

$a=5-2=3,b=9-3=6$ and $c=7-5=2$

So, the length of diagonal of a parallelopiped

$\begin{array}{c}=\sqrt{a^2+b^2+c^2}\\ =\sqrt{9+36+4}\\ =7units\end{array}$