Question

The shortest distances of the point $(1,2,3)$ from the axis $X,Y$and $Z$ respectively are

• A. $1,2,3$
• B. $\sqrt{5},\sqrt{13},\sqrt{10}$
• C. $\sqrt{10},\sqrt{13},\sqrt{5}$
• D. $\sqrt{13},\sqrt{10},\sqrt{5}$

Answer 1

The correct option is D

$\sqrt{13},\sqrt{10},\sqrt{5}$

Explanation for the correct option.

Find the shortest distance of the point from all three axes.

The distance of the point $(1,2,3)$ from $X-$axis is

$$\begin{gathered} =\sqrt{y^2+z^2} \\ =\sqrt{4+9} \\ =\sqrt{13}units \end{gathered}$$

The distance of the point $(1,2,3)$ from$Y-$axis is

$$\begin{gathered} =\sqrt{x^2+z^2} \\ =\sqrt{1+9} \\ =\sqrt{10}units \end{gathered}$$

The distance of the point $(1,2,3)$ from $Z-$axis is

$$\begin{gathered} =\sqrt{x^2+y^2} \\ =\sqrt{1+4} \\ =\sqrt{5}units \end{gathered}$$

Hence, option $D$ is the correct answer.