JEE Exam > JEE Questions > If the sum of the squares of the distances of...
Start Learning for Free
If the sum of the squares of the distances of a point from the three coordinate axes be 36, then its distance from the origin is
- a)6
- b)3√2
- c)2√3
- d)6√2
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If the sum of the squares of the distances of apoint from the three co...
Let (x,y,z) be the point.
Given sum of the squares of distance from point to the axes is 36.
⇒(x2+y2)+(y2+z2)+(z2+x2)=36
⇒2(x2+y2+z2)=36⇒x2+y2+z2=18
So the distance of the point from the origin is =3(2)1/2
Given sum of the squares of distance from point to the axes is 36.
⇒(x2+y2)+(y2+z2)+(z2+x2)=36
⇒2(x2+y2+z2)=36⇒x2+y2+z2=18
So the distance of the point from the origin is =3(2)1/2
Free Test
FREE
| Start Free Test |
Community Answer
If the sum of the squares of the distances of apoint from the three co...
Let the coordinates of the point be $(x,y,z)$. Then we have \begin{align*}
x^2+y^2+z^2 &= 36 \\
x^2+y^2 &= 36-z^2 \\
y^2+z^2 &= 36-x^2 \\
z^2+x^2 &= 36-y^2 \\
\end{align*} Adding all of these equations, we get $2(x^2+y^2+z^2) = 108$, which simplifies to $x^2+y^2+z^2 = 54$. Substituting this back into the original equation, we get $54 = 36$-$z^2$, so $z^2 = 18$. Therefore, the distance from the origin is $\sqrt{x^2+y^2+z^2} = \sqrt{54} = \boxed{3\sqrt{6}}$.
x^2+y^2+z^2 &= 36 \\
x^2+y^2 &= 36-z^2 \\
y^2+z^2 &= 36-x^2 \\
z^2+x^2 &= 36-y^2 \\
\end{align*} Adding all of these equations, we get $2(x^2+y^2+z^2) = 108$, which simplifies to $x^2+y^2+z^2 = 54$. Substituting this back into the original equation, we get $54 = 36$-$z^2$, so $z^2 = 18$. Therefore, the distance from the origin is $\sqrt{x^2+y^2+z^2} = \sqrt{54} = \boxed{3\sqrt{6}}$.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
If the sum of the squares of the distances of apoint from the three coordinate axes be 36, then itsdistance from the origin isa)6b)3√2c)2√3d)6√2Correct answer is option 'B'. Can you explain this answer?
Question Description
If the sum of the squares of the distances of apoint from the three coordinate axes be 36, then itsdistance from the origin isa)6b)3√2c)2√3d)6√2Correct answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If the sum of the squares of the distances of apoint from the three coordinate axes be 36, then itsdistance from the origin isa)6b)3√2c)2√3d)6√2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the sum of the squares of the distances of apoint from the three coordinate axes be 36, then itsdistance from the origin isa)6b)3√2c)2√3d)6√2Correct answer is option 'B'. Can you explain this answer?.
If the sum of the squares of the distances of apoint from the three coordinate axes be 36, then itsdistance from the origin isa)6b)3√2c)2√3d)6√2Correct answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If the sum of the squares of the distances of apoint from the three coordinate axes be 36, then itsdistance from the origin isa)6b)3√2c)2√3d)6√2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the sum of the squares of the distances of apoint from the three coordinate axes be 36, then itsdistance from the origin isa)6b)3√2c)2√3d)6√2Correct answer is option 'B'. Can you explain this answer?.
Solutions for If the sum of the squares of the distances of apoint from the three coordinate axes be 36, then itsdistance from the origin isa)6b)3√2c)2√3d)6√2Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of If the sum of the squares of the distances of apoint from the three coordinate axes be 36, then itsdistance from the origin isa)6b)3√2c)2√3d)6√2Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If the sum of the squares of the distances of apoint from the three coordinate axes be 36, then itsdistance from the origin isa)6b)3√2c)2√3d)6√2Correct answer is option 'B'. Can you explain this answer?, a detailed solution for If the sum of the squares of the distances of apoint from the three coordinate axes be 36, then itsdistance from the origin isa)6b)3√2c)2√3d)6√2Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of If the sum of the squares of the distances of apoint from the three coordinate axes be 36, then itsdistance from the origin isa)6b)3√2c)2√3d)6√2Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If the sum of the squares of the distances of apoint from the three coordinate axes be 36, then itsdistance from the origin isa)6b)3√2c)2√3d)6√2Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup