Question

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

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

Answer 1

The correct option is B

$7$units

Explanation for correct option:

Find the distance between given two points which are parallel to the coordinate planes.

Given coordinates are, $A(2,3,5)$ & $B(5,9,7)$

Distance between two points is given by,

$\mathit{D}\mathbf{=}\sqrt{{\mathbf{(}{\mathbf{x}}_{\mathbf{1}}\mathbf{-}{\mathbf{x}}_{\mathbf{2}}\mathbf{)}}^{\mathbf{2}}\mathbf{+}{\mathbf{(}{\mathbf{y}}_{\mathbf{1}}\mathbf{-}{\mathbf{y}}_{\mathbf{2}}\mathbf{)}}^{\mathbf{2}}\mathbf{+}{\mathbf{(}{\mathbf{z}}_{\mathbf{1}}\mathbf{-}{\mathbf{z}}_{\mathbf{2}}\mathbf{)}}^{\mathbf{2}}}$

We use the above formulae to calculate the distance,

Here,

$$\begin{gathered} x_1=2,x_2=5 \\ {y}_1=3,y_2=9 \\ {z}_1=5,z_2=7 \end{gathered}$$

Now, put the value in distance formula.

The distance between given two points:

$$\begin{gathered} AB=\sqrt{{(2-5)}^2+{(3-9)}^2+{(5-7)}^2} \\ AB=\sqrt{9+36+4} \\ AB=\sqrt{49} \\ AB=7units \end{gathered}$$

Therefore, Option $\left(B\right)$ is the correct answer.