JEE Exam > JEE Questions > A point moves so that the sum of the squares ...
Start Learning for Free
A point moves so that the sum of the squares of its distances from the six faces of a cube given by x = ± 1, y = ± 1, z = ± 1 is 10 units. The locus of the point is
- a)x2 + y2 + z2 = 1
- b)x2 + y2 + z2 = 2
- c)x + y + z = 1
- d)x + y + z = 2
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A point moves so that the sum of the squares ofits distances from the ...
Let the point be (x,y,z)
Distance of this point from x = 1 is |x -1| and from x = +1 is |x + 1|. Similarly you can find the distance from the other faces. The sum of squares of distances will be,
(x - 1)^2 + (x + 1)^2 + (y - 1)^2 + (y + 1)^2 + (z - 1)^2 + (z + 1)^2 = 10
2(x^2 + y^2 + z^2 ) + 6 = 10
x^2 + y^2 + z^2 = 2
Distance of this point from x = 1 is |x -1| and from x = +1 is |x + 1|. Similarly you can find the distance from the other faces. The sum of squares of distances will be,
(x - 1)^2 + (x + 1)^2 + (y - 1)^2 + (y + 1)^2 + (z - 1)^2 + (z + 1)^2 = 10
2(x^2 + y^2 + z^2 ) + 6 = 10
x^2 + y^2 + z^2 = 2
Free Test
FREE
| Start Free Test |
Community Answer
A point moves so that the sum of the squares ofits distances from the ...
Let's denote the point as P(x, y, z) and the cube as ABCDEFGH, where A = (0,0,0) is the origin and the cube has side length L.
To find the sum of the squares of the distances from P to the six faces of the cube, we can calculate the distance from P to each face individually and then square and sum those distances.
1. The distance from P to face ABCD:
Since P has coordinates (x, y, z), its x-coordinate must satisfy 0 ≤ x ≤ L. Therefore, the distance from P to face ABCD is |x - 0| = x.
2. The distance from P to face EFGH:
Since P has coordinates (x, y, z), its x-coordinate must satisfy 0 ≤ x ≤ L. Therefore, the distance from P to face EFGH is |x - L| = L - x.
3. The distance from P to face ABFE:
Since P has coordinates (x, y, z), its y-coordinate must satisfy 0 ≤ y ≤ L. Therefore, the distance from P to face ABFE is |y - 0| = y.
4. The distance from P to face DCGH:
Since P has coordinates (x, y, z), its y-coordinate must satisfy 0 ≤ y ≤ L. Therefore, the distance from P to face DCGH is |y - L| = L - y.
5. The distance from P to face AEDH:
Since P has coordinates (x, y, z), its z-coordinate must satisfy 0 ≤ z ≤ L. Therefore, the distance from P to face AEDH is |z - 0| = z.
6. The distance from P to face BFGC:
Since P has coordinates (x, y, z), its z-coordinate must satisfy 0 ≤ z ≤ L. Therefore, the distance from P to face BFGC is |z - L| = L - z.
Now, we can square and sum these distances:
x^2 + (L - x)^2 + y^2 + (L - y)^2 + z^2 + (L - z)^2
Expanding and simplifying, we get:
2x^2 + 2y^2 + 2z^2 - 2xL - 2yL - 2zL + 3L^2
Therefore, the sum of the squares of the distances from P to the six faces of the cube is 2x^2 + 2y^2 + 2z^2 - 2xL - 2yL - 2zL + 3L^2.
To find the sum of the squares of the distances from P to the six faces of the cube, we can calculate the distance from P to each face individually and then square and sum those distances.
1. The distance from P to face ABCD:
Since P has coordinates (x, y, z), its x-coordinate must satisfy 0 ≤ x ≤ L. Therefore, the distance from P to face ABCD is |x - 0| = x.
2. The distance from P to face EFGH:
Since P has coordinates (x, y, z), its x-coordinate must satisfy 0 ≤ x ≤ L. Therefore, the distance from P to face EFGH is |x - L| = L - x.
3. The distance from P to face ABFE:
Since P has coordinates (x, y, z), its y-coordinate must satisfy 0 ≤ y ≤ L. Therefore, the distance from P to face ABFE is |y - 0| = y.
4. The distance from P to face DCGH:
Since P has coordinates (x, y, z), its y-coordinate must satisfy 0 ≤ y ≤ L. Therefore, the distance from P to face DCGH is |y - L| = L - y.
5. The distance from P to face AEDH:
Since P has coordinates (x, y, z), its z-coordinate must satisfy 0 ≤ z ≤ L. Therefore, the distance from P to face AEDH is |z - 0| = z.
6. The distance from P to face BFGC:
Since P has coordinates (x, y, z), its z-coordinate must satisfy 0 ≤ z ≤ L. Therefore, the distance from P to face BFGC is |z - L| = L - z.
Now, we can square and sum these distances:
x^2 + (L - x)^2 + y^2 + (L - y)^2 + z^2 + (L - z)^2
Expanding and simplifying, we get:
2x^2 + 2y^2 + 2z^2 - 2xL - 2yL - 2zL + 3L^2
Therefore, the sum of the squares of the distances from P to the six faces of the cube is 2x^2 + 2y^2 + 2z^2 - 2xL - 2yL - 2zL + 3L^2.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
A point moves so that the sum of the squares ofits distances from the six faces of a cube given byx = ± 1, y = ± 1, z = ± 1 is 10 units. The locus of thepoint isa)x2+ y2+ z2= 1b)x2+ y2+ z2= 2c)x + y + z = 1d)x + y + z = 2Correct answer is option 'B'. Can you explain this answer?
Question Description
A point moves so that the sum of the squares ofits distances from the six faces of a cube given byx = ± 1, y = ± 1, z = ± 1 is 10 units. The locus of thepoint isa)x2+ y2+ z2= 1b)x2+ y2+ z2= 2c)x + y + z = 1d)x + y + z = 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 A point moves so that the sum of the squares ofits distances from the six faces of a cube given byx = ± 1, y = ± 1, z = ± 1 is 10 units. The locus of thepoint isa)x2+ y2+ z2= 1b)x2+ y2+ z2= 2c)x + y + z = 1d)x + y + z = 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 A point moves so that the sum of the squares ofits distances from the six faces of a cube given byx = ± 1, y = ± 1, z = ± 1 is 10 units. The locus of thepoint isa)x2+ y2+ z2= 1b)x2+ y2+ z2= 2c)x + y + z = 1d)x + y + z = 2Correct answer is option 'B'. Can you explain this answer?.
A point moves so that the sum of the squares ofits distances from the six faces of a cube given byx = ± 1, y = ± 1, z = ± 1 is 10 units. The locus of thepoint isa)x2+ y2+ z2= 1b)x2+ y2+ z2= 2c)x + y + z = 1d)x + y + z = 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 A point moves so that the sum of the squares ofits distances from the six faces of a cube given byx = ± 1, y = ± 1, z = ± 1 is 10 units. The locus of thepoint isa)x2+ y2+ z2= 1b)x2+ y2+ z2= 2c)x + y + z = 1d)x + y + z = 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 A point moves so that the sum of the squares ofits distances from the six faces of a cube given byx = ± 1, y = ± 1, z = ± 1 is 10 units. The locus of thepoint isa)x2+ y2+ z2= 1b)x2+ y2+ z2= 2c)x + y + z = 1d)x + y + z = 2Correct answer is option 'B'. Can you explain this answer?.
Solutions for A point moves so that the sum of the squares ofits distances from the six faces of a cube given byx = ± 1, y = ± 1, z = ± 1 is 10 units. The locus of thepoint isa)x2+ y2+ z2= 1b)x2+ y2+ z2= 2c)x + y + z = 1d)x + y + z = 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 A point moves so that the sum of the squares ofits distances from the six faces of a cube given byx = ± 1, y = ± 1, z = ± 1 is 10 units. The locus of thepoint isa)x2+ y2+ z2= 1b)x2+ y2+ z2= 2c)x + y + z = 1d)x + y + z = 2Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A point moves so that the sum of the squares ofits distances from the six faces of a cube given byx = ± 1, y = ± 1, z = ± 1 is 10 units. The locus of thepoint isa)x2+ y2+ z2= 1b)x2+ y2+ z2= 2c)x + y + z = 1d)x + y + z = 2Correct answer is option 'B'. Can you explain this answer?, a detailed solution for A point moves so that the sum of the squares ofits distances from the six faces of a cube given byx = ± 1, y = ± 1, z = ± 1 is 10 units. The locus of thepoint isa)x2+ y2+ z2= 1b)x2+ y2+ z2= 2c)x + y + z = 1d)x + y + z = 2Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of A point moves so that the sum of the squares ofits distances from the six faces of a cube given byx = ± 1, y = ± 1, z = ± 1 is 10 units. The locus of thepoint isa)x2+ y2+ z2= 1b)x2+ y2+ z2= 2c)x + y + z = 1d)x + y + z = 2Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A point moves so that the sum of the squares ofits distances from the six faces of a cube given byx = ± 1, y = ± 1, z = ± 1 is 10 units. The locus of thepoint isa)x2+ y2+ z2= 1b)x2+ y2+ z2= 2c)x + y + z = 1d)x + y + z = 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