Question

If the sum of the squares of the distance of a point from the three co-ordinate axes be 36,then its distance from origin

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

Answer 1

The correct option is B

$3\sqrt{2}$

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
$\sqrt{x^2+y^2+z^2}=\sqrt{18}=3\sqrt{2}.$