Question

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

(a) $2\sqrt{3}$

(b) $3\sqrt{2}$

(c) $\sqrt{2}$

(d) $\sqrt{3}$

Answer 1

Let A be given by (5, 8, 10) and B be given by (3, 6, 8)
then by distance formula,
$\begin{array}{rcl}AB& =& \sqrt{{\left(5-3\right)}^2+{\left(8-6\right)}^2+{\left(10-8\right)}^2}\\ & =& \sqrt{4+4+4}\\ & =& \sqrt{12}\\ & =& 2\sqrt{3}\\ & & \end{array}$
i.e the length of diagonal of parallelopiped is $2\sqrt{3}$.

Hence, the correct answer is option A.