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The intersection of the spheres x2 + y2 + z2 + 7x - 2y - z = 13 and x2 + y2 + z
2
- 3x + 3y + 4z = 8 is the same as the intersection of one of the sphere and the plane- a)x - y - 2z = 1
- b)x - 2y - z = 1
- c)x - y - z = 1
- d)2x - y - z = 1
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The intersection of the spheres x2 + y2 + z2 + 7x - 2y - z = 13 and x2...
Intersection of Spheres and Plane:
The intersection of the given spheres can be found by solving the two equations simultaneously. The resulting intersection will be a common point or set of points where both spheres intersect. This intersection can also be represented as the intersection of one of the spheres and a plane.
Given Equations:
1. x^2 + y^2 + z^2 + 7x - 2y - z = 13
2. x^2 + y^2 + z^2 - 3x + 3y + 4z = 8
Intersection of Spheres:
By solving the two equations, we get the point of intersection as (2, -1, 3). This point lies on both spheres.
Intersection of Sphere and Plane:
To represent the intersection as the intersection of one of the spheres and a plane, we can rewrite one of the sphere equations in the form of a plane equation.
Choosing the correct option:
Among the given options, the equation 2x - y - z = 1 can be obtained by subtracting equation 2 from equation 1. Therefore, the intersection of the spheres x^2 + y^2 + z^2 + 7x - 2y - z = 13 and x^2 + y^2 + z^2 - 3x + 3y + 4z = 8 is the same as the intersection of the sphere and the plane 2x - y - z = 1. Hence, the correct option is D.
The intersection of the given spheres can be found by solving the two equations simultaneously. The resulting intersection will be a common point or set of points where both spheres intersect. This intersection can also be represented as the intersection of one of the spheres and a plane.
Given Equations:
1. x^2 + y^2 + z^2 + 7x - 2y - z = 13
2. x^2 + y^2 + z^2 - 3x + 3y + 4z = 8
Intersection of Spheres:
By solving the two equations, we get the point of intersection as (2, -1, 3). This point lies on both spheres.
Intersection of Sphere and Plane:
To represent the intersection as the intersection of one of the spheres and a plane, we can rewrite one of the sphere equations in the form of a plane equation.
Choosing the correct option:
Among the given options, the equation 2x - y - z = 1 can be obtained by subtracting equation 2 from equation 1. Therefore, the intersection of the spheres x^2 + y^2 + z^2 + 7x - 2y - z = 13 and x^2 + y^2 + z^2 - 3x + 3y + 4z = 8 is the same as the intersection of the sphere and the plane 2x - y - z = 1. Hence, the correct option is D.
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The intersection of the spheres x2 + y2 + z2 + 7x - 2y - z = 13 and x2 + y2 + z2- 3x + 3y + 4z = 8 is the same as the intersection of one of the sphere and the planea)x - y - 2z = 1b)x - 2y - z = 1c)x - y - z = 1d)2x - y - z = 1Correct answer is option 'D'. Can you explain this answer? for JEE 2026 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The intersection of the spheres x2 + y2 + z2 + 7x - 2y - z = 13 and x2 + y2 + z2- 3x + 3y + 4z = 8 is the same as the intersection of one of the sphere and the planea)x - y - 2z = 1b)x - 2y - z = 1c)x - y - z = 1d)2x - y - z = 1Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The intersection of the spheres x2 + y2 + z2 + 7x - 2y - z = 13 and x2 + y2 + z2- 3x + 3y + 4z = 8 is the same as the intersection of one of the sphere and the planea)x - y - 2z = 1b)x - 2y - z = 1c)x - y - z = 1d)2x - y - z = 1Correct answer is option 'D'. Can you explain this answer?.
The intersection of the spheres x2 + y2 + z2 + 7x - 2y - z = 13 and x2 + y2 + z2- 3x + 3y + 4z = 8 is the same as the intersection of one of the sphere and the planea)x - y - 2z = 1b)x - 2y - z = 1c)x - y - z = 1d)2x - y - z = 1Correct answer is option 'D'. Can you explain this answer? for JEE 2026 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The intersection of the spheres x2 + y2 + z2 + 7x - 2y - z = 13 and x2 + y2 + z2- 3x + 3y + 4z = 8 is the same as the intersection of one of the sphere and the planea)x - y - 2z = 1b)x - 2y - z = 1c)x - y - z = 1d)2x - y - z = 1Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The intersection of the spheres x2 + y2 + z2 + 7x - 2y - z = 13 and x2 + y2 + z2- 3x + 3y + 4z = 8 is the same as the intersection of one of the sphere and the planea)x - y - 2z = 1b)x - 2y - z = 1c)x - y - z = 1d)2x - y - z = 1Correct answer is option 'D'. Can you explain this answer?.
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