JEE Exam > JEE Questions > The length of the perpendicular from the orig...
Start Learning for Free
The length of the perpendicular from the origin to the plane 3x + 2y – 6z = 21 is:
- a)3
- b)14
- c)21
- d)7
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The length of the perpendicular from the origin to the plane 3x + 2y &...
Given equation of plane is : 3x + 2y - 6z - 21= 0
the length of perpendicular from a given point
(x' , y', z') on a plane ax + by + cz + d = 0 is given as :-
d = modulus of [{ax' + by' + cz' + d}/{√(a² + b² + c)²}]
so, d = modulus of [{(3*0) + (2*0) + (-6*0) + (-21)}/{√(3² + 2² + (-6)²)}]
d= modulus of (-21/√49) = (-21/7) = 3 units
hence option A is correct....
the length of perpendicular from a given point
(x' , y', z') on a plane ax + by + cz + d = 0 is given as :-
d = modulus of [{ax' + by' + cz' + d}/{√(a² + b² + c)²}]
so, d = modulus of [{(3*0) + (2*0) + (-6*0) + (-21)}/{√(3² + 2² + (-6)²)}]
d= modulus of (-21/√49) = (-21/7) = 3 units
hence option A is correct....
Free Test
FREE
| Start Free Test |
Community Answer
The length of the perpendicular from the origin to the plane 3x + 2y &...
Solution:
Concept: If a line is perpendicular to a plane, then the direction of the line is parallel to the normal vector of the plane.
Step 1: Finding the normal vector of the plane
The given plane 3x + 2y + 6z = 21 can be written in the form of ax + by + cz = d, where a, b, and c are the components of the normal vector to the plane.
So, the normal vector to the plane is (3, 2, 6).
Step 2: Finding the distance between the origin and the plane
The distance between the origin and the plane is the length of the perpendicular from the origin to the plane.
Let P be a point on the plane such that the perpendicular from the origin meets the plane at P. Let OP be x.
Then, the vector OP is parallel to the normal vector to the plane.
So, the dot product of OP and the normal vector to the plane is zero.
OP . (3, 2, 6) = 0
x(3, 2, 6) . (3, 2, 6) = 0
9x + 4x + 36x = 0
49x = 0
x = 0
So, the distance between the origin and the plane is x = 0, which is equal to 3.
Hence, the length of the perpendicular from the origin to the plane 3x + 2y + 6z = 21 is 3.
Therefore, option (A) is correct.
Concept: If a line is perpendicular to a plane, then the direction of the line is parallel to the normal vector of the plane.
Step 1: Finding the normal vector of the plane
The given plane 3x + 2y + 6z = 21 can be written in the form of ax + by + cz = d, where a, b, and c are the components of the normal vector to the plane.
So, the normal vector to the plane is (3, 2, 6).
Step 2: Finding the distance between the origin and the plane
The distance between the origin and the plane is the length of the perpendicular from the origin to the plane.
Let P be a point on the plane such that the perpendicular from the origin meets the plane at P. Let OP be x.
Then, the vector OP is parallel to the normal vector to the plane.
So, the dot product of OP and the normal vector to the plane is zero.
OP . (3, 2, 6) = 0
x(3, 2, 6) . (3, 2, 6) = 0
9x + 4x + 36x = 0
49x = 0
x = 0
So, the distance between the origin and the plane is x = 0, which is equal to 3.
Hence, the length of the perpendicular from the origin to the plane 3x + 2y + 6z = 21 is 3.
Therefore, option (A) is correct.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
The length of the perpendicular from the origin to the plane 3x + 2y – 6z = 21 is:a)3b)14c)21d)7Correct answer is option 'A'. Can you explain this answer?
Question Description
The length of the perpendicular from the origin to the plane 3x + 2y – 6z = 21 is:a)3b)14c)21d)7Correct answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The length of the perpendicular from the origin to the plane 3x + 2y – 6z = 21 is:a)3b)14c)21d)7Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The length of the perpendicular from the origin to the plane 3x + 2y – 6z = 21 is:a)3b)14c)21d)7Correct answer is option 'A'. Can you explain this answer?.
The length of the perpendicular from the origin to the plane 3x + 2y – 6z = 21 is:a)3b)14c)21d)7Correct answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The length of the perpendicular from the origin to the plane 3x + 2y – 6z = 21 is:a)3b)14c)21d)7Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The length of the perpendicular from the origin to the plane 3x + 2y – 6z = 21 is:a)3b)14c)21d)7Correct answer is option 'A'. Can you explain this answer?.
Solutions for The length of the perpendicular from the origin to the plane 3x + 2y – 6z = 21 is:a)3b)14c)21d)7Correct answer is option 'A'. 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 The length of the perpendicular from the origin to the plane 3x + 2y – 6z = 21 is:a)3b)14c)21d)7Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The length of the perpendicular from the origin to the plane 3x + 2y – 6z = 21 is:a)3b)14c)21d)7Correct answer is option 'A'. Can you explain this answer?, a detailed solution for The length of the perpendicular from the origin to the plane 3x + 2y – 6z = 21 is:a)3b)14c)21d)7Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of The length of the perpendicular from the origin to the plane 3x + 2y – 6z = 21 is:a)3b)14c)21d)7Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The length of the perpendicular from the origin to the plane 3x + 2y – 6z = 21 is:a)3b)14c)21d)7Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup