Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

For a point $P(x,y,z)$, the distance from the x-axis is $\sqrt{y^2+z^2}$.

The distance from the y-axis is $\sqrt{x^2+z^2}$.

The distance from the z-axis is $\sqrt{x^2+y^2}$.

The sum of the squares of the distances from the three coordinate axes is $324$.

$(y^2+z^2)+(x^2+z^2)+(x^2+y^2)=324$

$2(x^2+y^2+z^2)=324$

$x^2+y^2+z^2=162$

The distance of point $P$ from the origin is $\sqrt{x^2+y^2+z^2}$.

$\sqrt{x^2+y^2+z^2}=\sqrt{162}=9\sqrt{2}$

Answer: $9\sqrt{2}$