Question

The extremities of a diagonal of a rectangular parallelopiped whose faces are parallel to the reference planes are $(-2,4,6)$ and $(3,16,6)$. The length of the base diagonal is

• A. $13$
• B. $\sqrt{13}$
• C. $2\sqrt{13}$
• D. $169$

Answer 1

The correct option is A $13$

By looking $(-2,4,6)$ and $(3,16,6)$ extremities of a diagonal both lie in same plane ($xy$- plane).

Base diagonal is diagonal joining these two extremities.

So, length of diagonal $=\sqrt{(3+2{)}^2+{(16-4)}^2+{(6-6)}^2}$
$=13$