JEE Exam > JEE Questions > If the lines x + 2ay + a = 0, x + 3by + b = ...
Start Learning for Free
If the lines x + 2ay + a = 0, x + 3by + b = 0, x + 4cy + c = 0 are concurrent, then a, b, c are in
- a)Arithmetic progression
- b)Geometric progression
- c)Harmonic progression
- d)Arithmetico-Geometric progression
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
If the lines x + 2ay + a = 0, x + 3by + b = 0, x + 4cy + c = 0 are co...
Gien lines are x + 2ay + a = 0, x + 3by + b = 0, x + 4cy + c = 0
Condition for the concurrency of lines,
Hence, a, b, c are in H.P.
Free Test
FREE
| Start Free Test |
Community Answer
If the lines x + 2ay + a = 0, x + 3by + b = 0, x + 4cy + c = 0 are co...
Concurrent Lines:
When three lines intersect at a common point, they are said to be concurrent. In this case, the lines x + 2ay + a = 0, x + 3by + b = 0, and x + 4cy + c = 0 are concurrent.
Using the concept of concurrency:
To determine the relationship between a, b, and c, we can use the concept of concurrency. When three lines are concurrent, the determinant of the coefficients of x, y, and the constant term in the equations of the lines is equal to zero.
Let's calculate the determinant:
| 1 2a a |
| 1 3b b | = 0
| 1 4c c |
Simplifying the determinant, we get:
(1)(3b)(c) + (2a)(b)(1) + (a)(1)(4c) - (1)(b)(4c) - (2a)(1)(c) - (a)(3b)(1) = 0
3bc + 2ab + 4ac - 4bc - 2ac - 3ab = 0
-3ab + ab + 3bc - 2ac + 4ac - 4bc = 0
-ab + 3bc + 2ac = 0
Harmonic Progression:
A harmonic progression is a sequence of numbers in which the reciprocals of the terms are in arithmetic progression.
Proving a, b, and c are in Harmonic Progression:
To prove that a, b, and c are in harmonic progression, we need to show that the reciprocals of a, b, and c are in arithmetic progression.
Taking the reciprocals of a, b, and c, we have:
1/a, 1/b, 1/c
Now, let's calculate the differences between consecutive terms:
(1/b) - (1/a) = (a - b)/(ab)
(1/c) - (1/b) = (b - c)/(bc)
Since the reciprocals of a, b, and c are in arithmetic progression, the differences between consecutive terms are constant. Therefore, a, b, and c are in harmonic progression.
Hence, the correct answer is option C) Harmonic progression.
When three lines intersect at a common point, they are said to be concurrent. In this case, the lines x + 2ay + a = 0, x + 3by + b = 0, and x + 4cy + c = 0 are concurrent.
Using the concept of concurrency:
To determine the relationship between a, b, and c, we can use the concept of concurrency. When three lines are concurrent, the determinant of the coefficients of x, y, and the constant term in the equations of the lines is equal to zero.
Let's calculate the determinant:
| 1 2a a |
| 1 3b b | = 0
| 1 4c c |
Simplifying the determinant, we get:
(1)(3b)(c) + (2a)(b)(1) + (a)(1)(4c) - (1)(b)(4c) - (2a)(1)(c) - (a)(3b)(1) = 0
3bc + 2ab + 4ac - 4bc - 2ac - 3ab = 0
-3ab + ab + 3bc - 2ac + 4ac - 4bc = 0
-ab + 3bc + 2ac = 0
Harmonic Progression:
A harmonic progression is a sequence of numbers in which the reciprocals of the terms are in arithmetic progression.
Proving a, b, and c are in Harmonic Progression:
To prove that a, b, and c are in harmonic progression, we need to show that the reciprocals of a, b, and c are in arithmetic progression.
Taking the reciprocals of a, b, and c, we have:
1/a, 1/b, 1/c
Now, let's calculate the differences between consecutive terms:
(1/b) - (1/a) = (a - b)/(ab)
(1/c) - (1/b) = (b - c)/(bc)
Since the reciprocals of a, b, and c are in arithmetic progression, the differences between consecutive terms are constant. Therefore, a, b, and c are in harmonic progression.
Hence, the correct answer is option C) Harmonic progression.
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
If the lines x + 2ay + a = 0, x + 3by + b = 0, x + 4cy + c = 0 are concurrent, then a, b, c are ina)Arithmetic progressionb)Geometric progressionc)Harmonic progressiond)Arithmetico-Geometric progressionCorrect answer is option 'C'. Can you explain this answer?
Question Description
If the lines x + 2ay + a = 0, x + 3by + b = 0, x + 4cy + c = 0 are concurrent, then a, b, c are ina)Arithmetic progressionb)Geometric progressionc)Harmonic progressiond)Arithmetico-Geometric progressionCorrect 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 If the lines x + 2ay + a = 0, x + 3by + b = 0, x + 4cy + c = 0 are concurrent, then a, b, c are ina)Arithmetic progressionb)Geometric progressionc)Harmonic progressiond)Arithmetico-Geometric progressionCorrect 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 If the lines x + 2ay + a = 0, x + 3by + b = 0, x + 4cy + c = 0 are concurrent, then a, b, c are ina)Arithmetic progressionb)Geometric progressionc)Harmonic progressiond)Arithmetico-Geometric progressionCorrect answer is option 'C'. Can you explain this answer?.
If the lines x + 2ay + a = 0, x + 3by + b = 0, x + 4cy + c = 0 are concurrent, then a, b, c are ina)Arithmetic progressionb)Geometric progressionc)Harmonic progressiond)Arithmetico-Geometric progressionCorrect 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 If the lines x + 2ay + a = 0, x + 3by + b = 0, x + 4cy + c = 0 are concurrent, then a, b, c are ina)Arithmetic progressionb)Geometric progressionc)Harmonic progressiond)Arithmetico-Geometric progressionCorrect 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 If the lines x + 2ay + a = 0, x + 3by + b = 0, x + 4cy + c = 0 are concurrent, then a, b, c are ina)Arithmetic progressionb)Geometric progressionc)Harmonic progressiond)Arithmetico-Geometric progressionCorrect answer is option 'C'. Can you explain this answer?.
Solutions for If the lines x + 2ay + a = 0, x + 3by + b = 0, x + 4cy + c = 0 are concurrent, then a, b, c are ina)Arithmetic progressionb)Geometric progressionc)Harmonic progressiond)Arithmetico-Geometric progressionCorrect answer is option 'C'. 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 lines x + 2ay + a = 0, x + 3by + b = 0, x + 4cy + c = 0 are concurrent, then a, b, c are ina)Arithmetic progressionb)Geometric progressionc)Harmonic progressiond)Arithmetico-Geometric progressionCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If the lines x + 2ay + a = 0, x + 3by + b = 0, x + 4cy + c = 0 are concurrent, then a, b, c are ina)Arithmetic progressionb)Geometric progressionc)Harmonic progressiond)Arithmetico-Geometric progressionCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for If the lines x + 2ay + a = 0, x + 3by + b = 0, x + 4cy + c = 0 are concurrent, then a, b, c are ina)Arithmetic progressionb)Geometric progressionc)Harmonic progressiond)Arithmetico-Geometric progressionCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of If the lines x + 2ay + a = 0, x + 3by + b = 0, x + 4cy + c = 0 are concurrent, then a, b, c are ina)Arithmetic progressionb)Geometric progressionc)Harmonic progressiond)Arithmetico-Geometric progressionCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If the lines x + 2ay + a = 0, x + 3by + b = 0, x + 4cy + c = 0 are concurrent, then a, b, c are ina)Arithmetic progressionb)Geometric progressionc)Harmonic progressiond)Arithmetico-Geometric progressionCorrect answer is option 'C'. 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
|
Follow Us
|
Signup to see your scores
go up
within 7 days!
within 7 days!
Takes less than 10 seconds to signup