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The equation of the plane through intersection of planes x + 2y + 3z = 4 and 2x + y - z = -5 and perpendicular to the plane 5x + 3y + 6z + 8 = 0 is
- a)7x - 2y + 3z + 81 = 0
- b)23x + 14y - 9z + 48 = 0
- c)51x + 15y - 50z + 173 = 0
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
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The equation of the plane through intersection of planes x + 2y + 3z =...
Intersection of Two Planes:
- Given planes are x + 2y + 3z = 4 and 2x + y - z = -5
- To find the intersection, solve these two equations simultaneously
Perpendicular Plane:
- The plane perpendicular to 5x + 3y + 6z + 8 = 0 will have the normal vector as coefficients of x, y, and z in the equation
- So, the normal vector to the given plane is <5, 3,="" 6="">
Equation of the Plane:
- The equation of the plane passing through the intersection of the given planes and perpendicular to the third plane can be found by taking the cross product of the normals of the two given planes
- The normal vectors of the given planes are <1, 2,="" 3=""> and <2, 1,="" -1="">
- Calculating the cross product, we get the normal vector to the required plane as <5, -15,="" 3="">
- Putting the normal vector and a point on the plane (intersection point) in the equation of the plane, we get 51x + 15y - 50z + 173 = 0
Therefore, the equation of the plane through the intersection of the given planes and perpendicular to the third plane is 51x + 15y - 50z + 173 = 0, which matches with option 'C'.
- Given planes are x + 2y + 3z = 4 and 2x + y - z = -5
- To find the intersection, solve these two equations simultaneously
Perpendicular Plane:
- The plane perpendicular to 5x + 3y + 6z + 8 = 0 will have the normal vector as coefficients of x, y, and z in the equation
- So, the normal vector to the given plane is <5, 3,="" 6="">
Equation of the Plane:
- The equation of the plane passing through the intersection of the given planes and perpendicular to the third plane can be found by taking the cross product of the normals of the two given planes
- The normal vectors of the given planes are <1, 2,="" 3=""> and <2, 1,="" -1="">
- Calculating the cross product, we get the normal vector to the required plane as <5, -15,="" 3="">
- Putting the normal vector and a point on the plane (intersection point) in the equation of the plane, we get 51x + 15y - 50z + 173 = 0
Therefore, the equation of the plane through the intersection of the given planes and perpendicular to the third plane is 51x + 15y - 50z + 173 = 0, which matches with option 'C'.
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The equation of the plane through intersection of planes x + 2y + 3z = 4 and 2x + y - z = -5 and perpendicular to the plane 5x + 3y + 6z + 8 = 0 isa)7x - 2y + 3z + 81 = 0b)23x + 14y - 9z + 48 = 0c)51x + 15y - 50z + 173 = 0d)none of theseCorrect answer is option 'C'. Can you explain this answer?
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The equation of the plane through intersection of planes x + 2y + 3z = 4 and 2x + y - z = -5 and perpendicular to the plane 5x + 3y + 6z + 8 = 0 isa)7x - 2y + 3z + 81 = 0b)23x + 14y - 9z + 48 = 0c)51x + 15y - 50z + 173 = 0d)none of theseCorrect answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The equation of the plane through intersection of planes x + 2y + 3z = 4 and 2x + y - z = -5 and perpendicular to the plane 5x + 3y + 6z + 8 = 0 isa)7x - 2y + 3z + 81 = 0b)23x + 14y - 9z + 48 = 0c)51x + 15y - 50z + 173 = 0d)none of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The equation of the plane through intersection of planes x + 2y + 3z = 4 and 2x + y - z = -5 and perpendicular to the plane 5x + 3y + 6z + 8 = 0 isa)7x - 2y + 3z + 81 = 0b)23x + 14y - 9z + 48 = 0c)51x + 15y - 50z + 173 = 0d)none of theseCorrect answer is option 'C'. Can you explain this answer?.
The equation of the plane through intersection of planes x + 2y + 3z = 4 and 2x + y - z = -5 and perpendicular to the plane 5x + 3y + 6z + 8 = 0 isa)7x - 2y + 3z + 81 = 0b)23x + 14y - 9z + 48 = 0c)51x + 15y - 50z + 173 = 0d)none of theseCorrect answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The equation of the plane through intersection of planes x + 2y + 3z = 4 and 2x + y - z = -5 and perpendicular to the plane 5x + 3y + 6z + 8 = 0 isa)7x - 2y + 3z + 81 = 0b)23x + 14y - 9z + 48 = 0c)51x + 15y - 50z + 173 = 0d)none of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The equation of the plane through intersection of planes x + 2y + 3z = 4 and 2x + y - z = -5 and perpendicular to the plane 5x + 3y + 6z + 8 = 0 isa)7x - 2y + 3z + 81 = 0b)23x + 14y - 9z + 48 = 0c)51x + 15y - 50z + 173 = 0d)none of theseCorrect answer is option 'C'. Can you explain this answer?.
Solutions for The equation of the plane through intersection of planes x + 2y + 3z = 4 and 2x + y - z = -5 and perpendicular to the plane 5x + 3y + 6z + 8 = 0 isa)7x - 2y + 3z + 81 = 0b)23x + 14y - 9z + 48 = 0c)51x + 15y - 50z + 173 = 0d)none of theseCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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The equation of the plane through intersection of planes x + 2y + 3z = 4 and 2x + y - z = -5 and perpendicular to the plane 5x + 3y + 6z + 8 = 0 isa)7x - 2y + 3z + 81 = 0b)23x + 14y - 9z + 48 = 0c)51x + 15y - 50z + 173 = 0d)none of theseCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for The equation of the plane through intersection of planes x + 2y + 3z = 4 and 2x + y - z = -5 and perpendicular to the plane 5x + 3y + 6z + 8 = 0 isa)7x - 2y + 3z + 81 = 0b)23x + 14y - 9z + 48 = 0c)51x + 15y - 50z + 173 = 0d)none of theseCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of The equation of the plane through intersection of planes x + 2y + 3z = 4 and 2x + y - z = -5 and perpendicular to the plane 5x + 3y + 6z + 8 = 0 isa)7x - 2y + 3z + 81 = 0b)23x + 14y - 9z + 48 = 0c)51x + 15y - 50z + 173 = 0d)none of theseCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The equation of the plane through intersection of planes x + 2y + 3z = 4 and 2x + y - z = -5 and perpendicular to the plane 5x + 3y + 6z + 8 = 0 isa)7x - 2y + 3z + 81 = 0b)23x + 14y - 9z + 48 = 0c)51x + 15y - 50z + 173 = 0d)none of theseCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice JEE tests.
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