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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=?
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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
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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=?
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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=?.
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