JEE Exam > JEE Questions > If a point R(4, y, z) lies on the line segmen...
Start Learning for Free
If a point R(4, y, z) lies on the line segment joining the points P (2,-3, 4) and Q(8, 0, 10), then the distance of R from the origin is:
- a)2√14
- b)6
- c)2√21
- d)√53
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
If a point R(4, y, z) lies on the line segment joining the points P (2...
Here, P, Q, R are collinear ⇒ 
Most Upvoted Answer
If a point R(4, y, z) lies on the line segment joining the points P (2...
The line segment joining P(2,-3,4) and Q(8,0,10) can be parameterized as follows:
x = 2 + t(8-2)
y = -3 + t(0-(-3))
z = 4 + t(10-4)
Simplifying these equations, we get:
x = 2 + 6t
y = -3 + 3t
z = 4 + 6t
Now we substitute the coordinates of point R(4,y,z) into these equations:
4 = 2 + 6t
y = -3 + 3t
z = 4 + 6t
Solving the first equation, we find t = 1/3.
Substituting this value of t into the second and third equations, we get:
y = -3 + 3(1/3) = 0
z = 4 + 6(1/3) = 6
So the coordinates of R are (4,0,6).
The distance of R from the origin can be found using the distance formula:
distance = √((x-0)^2 + (y-0)^2 + (z-0)^2)
= √(4^2 + 0^2 + 6^2)
= √(16 + 0 + 36)
= √52
≈ 7.211
Therefore, the distance of R from the origin is approximately 7.211.
x = 2 + t(8-2)
y = -3 + t(0-(-3))
z = 4 + t(10-4)
Simplifying these equations, we get:
x = 2 + 6t
y = -3 + 3t
z = 4 + 6t
Now we substitute the coordinates of point R(4,y,z) into these equations:
4 = 2 + 6t
y = -3 + 3t
z = 4 + 6t
Solving the first equation, we find t = 1/3.
Substituting this value of t into the second and third equations, we get:
y = -3 + 3(1/3) = 0
z = 4 + 6(1/3) = 6
So the coordinates of R are (4,0,6).
The distance of R from the origin can be found using the distance formula:
distance = √((x-0)^2 + (y-0)^2 + (z-0)^2)
= √(4^2 + 0^2 + 6^2)
= √(16 + 0 + 36)
= √52
≈ 7.211
Therefore, the distance of R from the origin is approximately 7.211.
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 a point R(4, y, z) lies on the line segment joining the points P (2,-3, 4) and Q(8, 0, 10), then the distance of R from the origin is:a)2√14b)6c)2√21d)√53Correct answer is option 'A'. Can you explain this answer?
Question Description
If a point R(4, y, z) lies on the line segment joining the points P (2,-3, 4) and Q(8, 0, 10), then the distance of R from the origin is:a)2√14b)6c)2√21d)√53Correct answer is option 'A'. 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 a point R(4, y, z) lies on the line segment joining the points P (2,-3, 4) and Q(8, 0, 10), then the distance of R from the origin is:a)2√14b)6c)2√21d)√53Correct answer is option 'A'. 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 a point R(4, y, z) lies on the line segment joining the points P (2,-3, 4) and Q(8, 0, 10), then the distance of R from the origin is:a)2√14b)6c)2√21d)√53Correct answer is option 'A'. Can you explain this answer?.
If a point R(4, y, z) lies on the line segment joining the points P (2,-3, 4) and Q(8, 0, 10), then the distance of R from the origin is:a)2√14b)6c)2√21d)√53Correct answer is option 'A'. 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 a point R(4, y, z) lies on the line segment joining the points P (2,-3, 4) and Q(8, 0, 10), then the distance of R from the origin is:a)2√14b)6c)2√21d)√53Correct answer is option 'A'. 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 a point R(4, y, z) lies on the line segment joining the points P (2,-3, 4) and Q(8, 0, 10), then the distance of R from the origin is:a)2√14b)6c)2√21d)√53Correct answer is option 'A'. Can you explain this answer?.
Solutions for If a point R(4, y, z) lies on the line segment joining the points P (2,-3, 4) and Q(8, 0, 10), then the distance of R from the origin is:a)2√14b)6c)2√21d)√53Correct 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 If a point R(4, y, z) lies on the line segment joining the points P (2,-3, 4) and Q(8, 0, 10), then the distance of R from the origin is:a)2√14b)6c)2√21d)√53Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If a point R(4, y, z) lies on the line segment joining the points P (2,-3, 4) and Q(8, 0, 10), then the distance of R from the origin is:a)2√14b)6c)2√21d)√53Correct answer is option 'A'. Can you explain this answer?, a detailed solution for If a point R(4, y, z) lies on the line segment joining the points P (2,-3, 4) and Q(8, 0, 10), then the distance of R from the origin is:a)2√14b)6c)2√21d)√53Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of If a point R(4, y, z) lies on the line segment joining the points P (2,-3, 4) and Q(8, 0, 10), then the distance of R from the origin is:a)2√14b)6c)2√21d)√53Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If a point R(4, y, z) lies on the line segment joining the points P (2,-3, 4) and Q(8, 0, 10), then the distance of R from the origin is:a)2√14b)6c)2√21d)√53Correct answer is option 'A'. 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!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup