JEE Exam > JEE Questions > can anyone hlp me with thiss...a vector a has...
Start Learning for Free
can anyone hlp me with thiss...a vector a has components 2p nd 1 with rspct 2 rectangular Cartesian coordinate system.this system is rotated through a certain angle about the origin in counter clockwise sense. if,with respect to new system ,a has components p+1 and 1.p=?
Most Upvoted Answer
can anyone hlp me with thiss...a vector a has components 2p nd 1 with ...
Transformation of Vector Components
To solve this problem, we need to understand how a vector's components change when the coordinate system is rotated about the origin. Let's break down the problem into smaller steps.
Step 1: Initial Vector Components
The vector 'a' has components 2p and 1 in the original rectangular Cartesian coordinate system. We can represent this vector as a = (2p, 1).
Step 2: Coordinate System Rotation
The coordinate system is rotated through a certain angle in the counterclockwise sense. Let's call this angle 'θ'.
Step 3: New Vector Components
After the rotation, the vector 'a' will have new components in the new coordinate system. Let's represent the new components as p and 1. We can write the new vector as a' = (p, 1).
Step 4: Relationship between Initial and New Components
To find the value of p, we need to establish a relationship between the initial and new components of the vector.
Step 5: Rotating the Coordinate System
When the coordinate system is rotated counterclockwise, the x and y axes of the new system are related to the original system by the following equations:
x' = x * cos(θ) - y * sin(θ)
y' = x * sin(θ) + y * cos(θ)
where (x, y) are the coordinates in the original system, and (x', y') are the coordinates in the new system.
Step 6: Applying the Transformation
Let's apply the transformation equations to the vector 'a' in the original system:
x' = 2p * cos(θ) - 1 * sin(θ) = p
y' = 2p * sin(θ) + 1 * cos(θ) = 1
Step 7: Solving for p
From the above equations, we can see that p = x' = 1.
Conclusion
Therefore, the value of p is 1. The vector 'a' with components 2p and 1 in the original system will have components p and 1 in the new system, where p = 1.
Note: The given angle of rotation 'θ' was not specified, so we cannot determine its exact value. However, the value of p does not depend on the angle of rotation.
To solve this problem, we need to understand how a vector's components change when the coordinate system is rotated about the origin. Let's break down the problem into smaller steps.
Step 1: Initial Vector Components
The vector 'a' has components 2p and 1 in the original rectangular Cartesian coordinate system. We can represent this vector as a = (2p, 1).
Step 2: Coordinate System Rotation
The coordinate system is rotated through a certain angle in the counterclockwise sense. Let's call this angle 'θ'.
Step 3: New Vector Components
After the rotation, the vector 'a' will have new components in the new coordinate system. Let's represent the new components as p and 1. We can write the new vector as a' = (p, 1).
Step 4: Relationship between Initial and New Components
To find the value of p, we need to establish a relationship between the initial and new components of the vector.
Step 5: Rotating the Coordinate System
When the coordinate system is rotated counterclockwise, the x and y axes of the new system are related to the original system by the following equations:
x' = x * cos(θ) - y * sin(θ)
y' = x * sin(θ) + y * cos(θ)
where (x, y) are the coordinates in the original system, and (x', y') are the coordinates in the new system.
Step 6: Applying the Transformation
Let's apply the transformation equations to the vector 'a' in the original system:
x' = 2p * cos(θ) - 1 * sin(θ) = p
y' = 2p * sin(θ) + 1 * cos(θ) = 1
Step 7: Solving for p
From the above equations, we can see that p = x' = 1.
Conclusion
Therefore, the value of p is 1. The vector 'a' with components 2p and 1 in the original system will have components p and 1 in the new system, where p = 1.
Note: The given angle of rotation 'θ' was not specified, so we cannot determine its exact value. However, the value of p does not depend on the angle of rotation.
Community Answer
can anyone hlp me with thiss...a vector a has components 2p nd 1 with ...
Since the axes are rotated, the magnitude of the vector won't change.
so √{(p+1)^2 + 1} = √{(2p)^2 + 1}
solving this one may get,
p = 1 or -1/3
so √{(p+1)^2 + 1} = √{(2p)^2 + 1}
solving this one may get,
p = 1 or -1/3
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
|
|
Top Courses for JEEView all
can anyone hlp me with thiss...a vector a has components 2p nd 1 with rspct 2 rectangular Cartesian coordinate system.this system is rotated through a certain angle about the origin in counter clockwise sense. if,with respect to new system ,a has components p+1 and 1.p=?
Question Description
can anyone hlp me with thiss...a vector a has components 2p nd 1 with rspct 2 rectangular Cartesian coordinate system.this system is rotated through a certain angle about the origin in counter clockwise sense. if,with respect to new system ,a has components p+1 and 1.p=? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about can anyone hlp me with thiss...a vector a has components 2p nd 1 with rspct 2 rectangular Cartesian coordinate system.this system is rotated through a certain angle about the origin in counter clockwise sense. if,with respect to new system ,a has components p+1 and 1.p=? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for can anyone hlp me with thiss...a vector a has components 2p nd 1 with rspct 2 rectangular Cartesian coordinate system.this system is rotated through a certain angle about the origin in counter clockwise sense. if,with respect to new system ,a has components p+1 and 1.p=?.
can anyone hlp me with thiss...a vector a has components 2p nd 1 with rspct 2 rectangular Cartesian coordinate system.this system is rotated through a certain angle about the origin in counter clockwise sense. if,with respect to new system ,a has components p+1 and 1.p=? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about can anyone hlp me with thiss...a vector a has components 2p nd 1 with rspct 2 rectangular Cartesian coordinate system.this system is rotated through a certain angle about the origin in counter clockwise sense. if,with respect to new system ,a has components p+1 and 1.p=? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for can anyone hlp me with thiss...a vector a has components 2p nd 1 with rspct 2 rectangular Cartesian coordinate system.this system is rotated through a certain angle about the origin in counter clockwise sense. if,with respect to new system ,a has components p+1 and 1.p=?.
Solutions for can anyone hlp me with thiss...a vector a has components 2p nd 1 with rspct 2 rectangular Cartesian coordinate system.this system is rotated through a certain angle about the origin in counter clockwise sense. if,with respect to new system ,a has components p+1 and 1.p=? 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 can anyone hlp me with thiss...a vector a has components 2p nd 1 with rspct 2 rectangular Cartesian coordinate system.this system is rotated through a certain angle about the origin in counter clockwise sense. if,with respect to new system ,a has components p+1 and 1.p=? defined & explained in the simplest way possible. Besides giving the explanation of
can anyone hlp me with thiss...a vector a has components 2p nd 1 with rspct 2 rectangular Cartesian coordinate system.this system is rotated through a certain angle about the origin in counter clockwise sense. if,with respect to new system ,a has components p+1 and 1.p=?, a detailed solution for can anyone hlp me with thiss...a vector a has components 2p nd 1 with rspct 2 rectangular Cartesian coordinate system.this system is rotated through a certain angle about the origin in counter clockwise sense. if,with respect to new system ,a has components p+1 and 1.p=? has been provided alongside types of can anyone hlp me with thiss...a vector a has components 2p nd 1 with rspct 2 rectangular Cartesian coordinate system.this system is rotated through a certain angle about the origin in counter clockwise sense. if,with respect to new system ,a has components p+1 and 1.p=? theory, EduRev gives you an
ample number of questions to practice can anyone hlp me with thiss...a vector a has components 2p nd 1 with rspct 2 rectangular Cartesian coordinate system.this system is rotated through a certain angle about the origin in counter clockwise sense. if,with respect to new system ,a has components p+1 and 1.p=? 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