Question

If the sum of the squares of the distance of a point from the three coordinate axes be $36$, then its distance from the origin is

• A. $6$ units
• B. $3$ $\sqrt{2}$ units
• C. $2$ $\sqrt{3}$ units
• D. none of these

Answer 1

Answer: (B)

$3$ $\sqrt{2}$ units

Let $(x,y,z)$ be the point.

Given sum of the squares of distance from point to the axes is $36$.

$\Rightarrow (x^2+y^2)+(y^2+z^2)+(z^2+x^2)=36$

$\Rightarrow 2(x^2+y^2+z^2)=36\Rightarrow x^2+y^2+z^2=18$

So the distance of the point from the origin is $=\sqrt{x^2+y^2+z^2}=3\sqrt{2}$
Hence, option B; is correct.