Three Dimensional Geometry Question 91
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 the origin is
Options:
A) 6
B) $ 3\sqrt{2} $
C) $ 2\sqrt{3} $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Let $ P,(x,,y,,z). $ Now under given condition, we get $ {{[ \sqrt{(x^{2}+y^{2})} ]}^{2}}+{{[ \sqrt{(y^{2}+z^{2})} ]}^{2}}+{{[ \sqrt{(z^{2}+x^{2})} ]}^{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} $ .
BETA
