JEE Exam > JEE Questions > In the following case, determine whether the ...
Start Learning for Free
In the following case, determine whether the given planes are parallel orperpendicular, and in case they are neither, find the angles between them. 2x + y + 3z – 2 = 0 and x – 2y + 5 = 0
- a)The planes are parallel
- b)The planes are at 45∘
- c)The planes are at 55∘
- d)The planes are perpendicular
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
In the following case, determine whether the given planes are parallel...
We have ,
2x + y + 3z – 2 = 0 and x – 2y + 5 = 0. Let θ be the angle between the planes , then
2x + y + 3z – 2 = 0 and x – 2y + 5 = 0. Let θ be the angle between the planes , then
Most Upvoted Answer
In the following case, determine whether the given planes are parallel...
Understanding the Given Planes
To determine the relationship between the two planes, we need to first rewrite their equations in a standard format and extract the normal vectors.
Plane Equations
1. First Plane:
The equation is given as 2x + y + 3z - 2 = 0.
The normal vector (N1) can be derived from the coefficients:
N1 = (2, 1, 3).
2. Second Plane:
The equation is x - 2y + 5 = 0, which can be rewritten as x - 2y + 0z + 5 = 0.
The normal vector (N2) can be derived as:
N2 = (1, -2, 0).
Checking for Parallelism
- Two planes are parallel if their normal vectors are scalar multiples of each other.
- Here, N1 = (2, 1, 3) and N2 = (1, -2, 0) are not scalar multiples.
- Thus, the planes are not parallel.
Checking for Perpendicularity
- Two planes are perpendicular if the dot product of their normal vectors equals zero.
- We calculate the dot product:
N1 • N2 = (2)(1) + (1)(-2) + (3)(0) = 2 - 2 + 0 = 0.
- Since the dot product is zero, the planes are perpendicular.
Conclusion
The given planes are neither parallel nor at a specified angle; they are indeed perpendicular to each other. Thus, the correct answer is option 'D'.
To determine the relationship between the two planes, we need to first rewrite their equations in a standard format and extract the normal vectors.
Plane Equations
1. First Plane:
The equation is given as 2x + y + 3z - 2 = 0.
The normal vector (N1) can be derived from the coefficients:
N1 = (2, 1, 3).
2. Second Plane:
The equation is x - 2y + 5 = 0, which can be rewritten as x - 2y + 0z + 5 = 0.
The normal vector (N2) can be derived as:
N2 = (1, -2, 0).
Checking for Parallelism
- Two planes are parallel if their normal vectors are scalar multiples of each other.
- Here, N1 = (2, 1, 3) and N2 = (1, -2, 0) are not scalar multiples.
- Thus, the planes are not parallel.
Checking for Perpendicularity
- Two planes are perpendicular if the dot product of their normal vectors equals zero.
- We calculate the dot product:
N1 • N2 = (2)(1) + (1)(-2) + (3)(0) = 2 - 2 + 0 = 0.
- Since the dot product is zero, the planes are perpendicular.
Conclusion
The given planes are neither parallel nor at a specified angle; they are indeed perpendicular to each other. Thus, the correct answer is option 'D'.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
In the following case, determine whether the given planes are parallel orperpendicular, and in case they are neither, find the angles between them. 2x + y + 3z – 2 = 0 and x – 2y + 5 = 0a)The planes are parallelb)The planes are at45∘c)The planes are at55∘d)The planes are perpendicularCorrect answer is option 'D'. Can you explain this answer?
Question Description
In the following case, determine whether the given planes are parallel orperpendicular, and in case they are neither, find the angles between them. 2x + y + 3z – 2 = 0 and x – 2y + 5 = 0a)The planes are parallelb)The planes are at45∘c)The planes are at55∘d)The planes are perpendicularCorrect answer is option 'D'. 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 In the following case, determine whether the given planes are parallel orperpendicular, and in case they are neither, find the angles between them. 2x + y + 3z – 2 = 0 and x – 2y + 5 = 0a)The planes are parallelb)The planes are at45∘c)The planes are at55∘d)The planes are perpendicularCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the following case, determine whether the given planes are parallel orperpendicular, and in case they are neither, find the angles between them. 2x + y + 3z – 2 = 0 and x – 2y + 5 = 0a)The planes are parallelb)The planes are at45∘c)The planes are at55∘d)The planes are perpendicularCorrect answer is option 'D'. Can you explain this answer?.
In the following case, determine whether the given planes are parallel orperpendicular, and in case they are neither, find the angles between them. 2x + y + 3z – 2 = 0 and x – 2y + 5 = 0a)The planes are parallelb)The planes are at45∘c)The planes are at55∘d)The planes are perpendicularCorrect answer is option 'D'. 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 In the following case, determine whether the given planes are parallel orperpendicular, and in case they are neither, find the angles between them. 2x + y + 3z – 2 = 0 and x – 2y + 5 = 0a)The planes are parallelb)The planes are at45∘c)The planes are at55∘d)The planes are perpendicularCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the following case, determine whether the given planes are parallel orperpendicular, and in case they are neither, find the angles between them. 2x + y + 3z – 2 = 0 and x – 2y + 5 = 0a)The planes are parallelb)The planes are at45∘c)The planes are at55∘d)The planes are perpendicularCorrect answer is option 'D'. Can you explain this answer?.
Solutions for In the following case, determine whether the given planes are parallel orperpendicular, and in case they are neither, find the angles between them. 2x + y + 3z – 2 = 0 and x – 2y + 5 = 0a)The planes are parallelb)The planes are at45∘c)The planes are at55∘d)The planes are perpendicularCorrect answer is option 'D'. 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 In the following case, determine whether the given planes are parallel orperpendicular, and in case they are neither, find the angles between them. 2x + y + 3z – 2 = 0 and x – 2y + 5 = 0a)The planes are parallelb)The planes are at45∘c)The planes are at55∘d)The planes are perpendicularCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
In the following case, determine whether the given planes are parallel orperpendicular, and in case they are neither, find the angles between them. 2x + y + 3z – 2 = 0 and x – 2y + 5 = 0a)The planes are parallelb)The planes are at45∘c)The planes are at55∘d)The planes are perpendicularCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for In the following case, determine whether the given planes are parallel orperpendicular, and in case they are neither, find the angles between them. 2x + y + 3z – 2 = 0 and x – 2y + 5 = 0a)The planes are parallelb)The planes are at45∘c)The planes are at55∘d)The planes are perpendicularCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of In the following case, determine whether the given planes are parallel orperpendicular, and in case they are neither, find the angles between them. 2x + y + 3z – 2 = 0 and x – 2y + 5 = 0a)The planes are parallelb)The planes are at45∘c)The planes are at55∘d)The planes are perpendicularCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice In the following case, determine whether the given planes are parallel orperpendicular, and in case they are neither, find the angles between them. 2x + y + 3z – 2 = 0 and x – 2y + 5 = 0a)The planes are parallelb)The planes are at45∘c)The planes are at55∘d)The planes are perpendicularCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
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!
within 7 days!
Takes less than 10 seconds to signup