Question

A point $P(1,2,3)$ is one vertex of a cuboid formed by the coordinate planes and the planes passing through $P$ and parallel to the coordinate planes.

What is the length of one of the diagonals of the cuboid?

• A. $\sqrt{10}$ units
• B. $\sqrt{14}$ units
• C. $4$ units
• D. $5$ units

Answer 1

Answer: (B)

$\sqrt{14}$ units

As the cuboid is formed by the coordinate planes and their parallel planes passing through $P$, we have two opposite vertices of the cuboid as $P$ and the origin. Hence, the length of diagonal is $\sqrt{1^2+2^2+3^2}=\sqrt{14}$ units.