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P(x,y,z) is such that its distance from x-axis is \sqrt{3}  from y-axis is \sqrt{5}  and from z-axis is 2, then x^{2}+y^{2}+z^{2}  equals 

  • Option 1)

    3

  • Option 2)

    4

  • Option 3)

    5

  • Option 4)

    6

 

Answers (1)

best_answer

As we have learned

Distance from Co-ordinate axes -

Consider a point  P(x,y,z)

Distance from X-axis is  \sqrt{y^{2}+z^{2}}

Distance from Y-axis is \sqrt{x^{2}+z^{2}}

Distance from Z-axis is \sqrt{x^{2}+y^{2}}

-

 

 Distance for X-axis =\sqrt{y^{2}+z^{2}} = \sqrt3 \Rightarrow y^{2}+z^{2}= 3

Distance for Y-axis = \sqrt{x^{2}+z^{2}} = \sqrt5 \Rightarrow x^{2}+z^{2}= 5

Distance for Z-axis =\sqrt{x^{2}+y^{2}} = 2 \Rightarrow x^{2}+y^{2}= 4

Adding all, we get 

2(x^{2}+y^{2}+z^{2}) = 12

\Rightarrow x^{2}+y^{2}+z^{2}=6

\therefore Option (D)

 


Option 1)

3

Option 2)

4

Option 3)

5

Option 4)

6

Posted by

Himanshu

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