Defence Exam > Defence Questions > consider the plane passing through the points...
Start Learning for Free
consider the plane passing through the points A (2,2,1), B (3,4,2) and C (7,0,6).
Which one of the following points lines on the plane ?
- a)( 1, 0, 0)
- b)( 1, 0, 1)
- c)(0,0,1)
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
consider the plane passing through the points A (2,2,1), B (3,4,2) and...
We know that, equation of plane passing through three non-col linear points
(x1, y1, z1,), (x2, y2, z2) and (x3, y3, Z3) is
Put the value of (x1, y1, z1), (x2, y2, z2) and (x3, y3, z3) we get
⇒ (x -2) (10+ 2)- (y-2 ) (5 -5 ) + (z -1 ) ( -2 -10) = 0
⇒12x- 12z= 12⇒x-z = 1
Hence the equation of plane parses through (1,0, 1)
(x1, y1, z1,), (x2, y2, z2) and (x3, y3, Z3) is
Put the value of (x1, y1, z1), (x2, y2, z2) and (x3, y3, z3) we get
⇒ (x -2) (10+ 2)- (y-2 ) (5 -5 ) + (z -1 ) ( -2 -10) = 0
⇒12x- 12z= 12⇒x-z = 1
Hence the equation of plane parses through (1,0, 1)
Most Upvoted Answer
consider the plane passing through the points A (2,2,1), B (3,4,2) and...
Analysis:
To determine which of the given points lies on the plane passing through points A, B, and C, we can use the equation of a plane in 3D space. The equation of a plane passing through three non-collinear points (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3) is given by:
Ax + By + Cz = D
where A, B, C are the coefficients of x, y, z respectively, and D is a constant.
Calculations:
Given points A(2,2,1), B(3,4,2), and C(7,0,6), we can find the coefficients A, B, C, and D by substituting the values of these points into the equation of the plane. After calculating, the equation of the plane passing through these points is:
x - 3y + z = 3
Check which point lies on the plane:
Now, we can check which of the given points lies on the plane by substituting their coordinates into the equation of the plane.
a) (1, 0, 0): 1 - 3(0) + 0 = 1 ≠ 3
b) (1, 0, 1): 1 - 3(0) + 1 = 2 ≠ 3
c) (0, 0, 1): 0 - 3(0) + 1 = 1 ≠ 3
Therefore, none of the points a), c), d) lie on the plane passing through points A, B, and C. The correct point that lies on the plane is option b) (1, 0, 1).
|
Explore Courses for Defence exam
|
|
Similar Defence Doubts
consider the plane passing through the points A (2,2,1), B (3,4,2) and C (7,0,6).Which one of the following points lines on the plane ?a)( 1, 0, 0)b)( 1, 0, 1)c)(0,0,1)d)None of theseCorrect answer is option 'B'. Can you explain this answer?
Question Description
consider the plane passing through the points A (2,2,1), B (3,4,2) and C (7,0,6).Which one of the following points lines on the plane ?a)( 1, 0, 0)b)( 1, 0, 1)c)(0,0,1)d)None of theseCorrect answer is option 'B'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about consider the plane passing through the points A (2,2,1), B (3,4,2) and C (7,0,6).Which one of the following points lines on the plane ?a)( 1, 0, 0)b)( 1, 0, 1)c)(0,0,1)d)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for consider the plane passing through the points A (2,2,1), B (3,4,2) and C (7,0,6).Which one of the following points lines on the plane ?a)( 1, 0, 0)b)( 1, 0, 1)c)(0,0,1)d)None of theseCorrect answer is option 'B'. Can you explain this answer?.
consider the plane passing through the points A (2,2,1), B (3,4,2) and C (7,0,6).Which one of the following points lines on the plane ?a)( 1, 0, 0)b)( 1, 0, 1)c)(0,0,1)d)None of theseCorrect answer is option 'B'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about consider the plane passing through the points A (2,2,1), B (3,4,2) and C (7,0,6).Which one of the following points lines on the plane ?a)( 1, 0, 0)b)( 1, 0, 1)c)(0,0,1)d)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for consider the plane passing through the points A (2,2,1), B (3,4,2) and C (7,0,6).Which one of the following points lines on the plane ?a)( 1, 0, 0)b)( 1, 0, 1)c)(0,0,1)d)None of theseCorrect answer is option 'B'. Can you explain this answer?.
Solutions for consider the plane passing through the points A (2,2,1), B (3,4,2) and C (7,0,6).Which one of the following points lines on the plane ?a)( 1, 0, 0)b)( 1, 0, 1)c)(0,0,1)d)None of theseCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Defence.
Download more important topics, notes, lectures and mock test series for Defence Exam by signing up for free.
Here you can find the meaning of consider the plane passing through the points A (2,2,1), B (3,4,2) and C (7,0,6).Which one of the following points lines on the plane ?a)( 1, 0, 0)b)( 1, 0, 1)c)(0,0,1)d)None of theseCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
consider the plane passing through the points A (2,2,1), B (3,4,2) and C (7,0,6).Which one of the following points lines on the plane ?a)( 1, 0, 0)b)( 1, 0, 1)c)(0,0,1)d)None of theseCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for consider the plane passing through the points A (2,2,1), B (3,4,2) and C (7,0,6).Which one of the following points lines on the plane ?a)( 1, 0, 0)b)( 1, 0, 1)c)(0,0,1)d)None of theseCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of consider the plane passing through the points A (2,2,1), B (3,4,2) and C (7,0,6).Which one of the following points lines on the plane ?a)( 1, 0, 0)b)( 1, 0, 1)c)(0,0,1)d)None of theseCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice consider the plane passing through the points A (2,2,1), B (3,4,2) and C (7,0,6).Which one of the following points lines on the plane ?a)( 1, 0, 0)b)( 1, 0, 1)c)(0,0,1)d)None of theseCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Defence tests.
|
|
Explore Courses for Defence 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
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup