Question

A point moves in such a way that sum of squares of its distances from the co-ordinate axis is 36, then distance of then given point from origin are ______.

Options

• 6

• `2sqrt(3)`

• `3sqrt(2)`

• `sqrt(6)`

Answer 1

A point moves in such a way that sum of squares of its distances from the co-ordinate axis is 36, then distance of then given point from origin are `underlinebb(3sqrt(2))`.

Explanation:

Distance of the point form 

x-axis = `sqrt(y^2 + z^2)`

y-axis = `sqrt(x^2 + z^2)`

z-axis = `sqrt(x^2 + y^2)`

Sum of squares = 36

⇒ 2(x² + y² + z²) = 36

⇒ x² + y² + z² = 18

Distance of this point from the origin

P = `sqrt(x^2 + y^2 + z^2)`

P = `sqrt(18)` = `3sqrt(2)`