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Q.
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
Three Dimensional Geometry
Solution:
Let $P(x, y, z)$ Now under given condition, we get
$\left[\sqrt{x^{2}+y^{2}}\right]^{2}+\left[\sqrt{y^{2}+z^{2}}\right]^{2}+\left[\sqrt{z^{2}+x^{2}}\right]^{2}=36$
$\Rightarrow x^{2}+y^{2}+z^{2}=18$
Then distance from origin to the point $(x, y, z)$ is
$\sqrt{x^{2}+y^{2}+z^{2}}=\sqrt{18}=3 \sqrt{2}$