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If the sum of the squares of the dist...

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

Text Solution

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Let P(x, y, z) be the point. Now, under the given condition,
`" "[sqrt(x^(2)+y^(2))]^(2)+[sqrt(y^(2)+z^(2))]^(2)+[sqrt(z^(2)+x^(2))]^(2)=36`
or `" "x^(2)+y^(2)+z^(2)=18`
Then distance from the origin to point (x, y, z) is
`" "sqrt(x^(2)+y^(2)+z^(2))=sqrt(18)=3sqrt(2)`
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