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Find the magnitude and direction of the resultant of two vectors of A vector and B vector in terms of their magnitudes and angle theta between them.?
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Find the magnitude and direction of the resultant of two vectors of A ...
Understanding the Resultant of Two Vectors
When dealing with two vectors, A and B, we can determine the resultant vector by considering both their magnitudes and the angle between them.
Magnitude of the Resultant Vector
To find the magnitude of the resultant vector (R), we use the formula:
- R = √(A² + B² + 2AB cos(θ))
Here,
- A and B are the magnitudes of the two vectors,
- θ is the angle between them,
- cos(θ) accounts for the direction of the vectors.
Direction of the Resultant Vector
The direction of the resultant vector can be calculated using the tangent function:
- tan(φ) = (B sin(θ)) / (A + B cos(θ))
Where φ is the angle the resultant vector makes with vector A.
Steps to Calculate the Resultant
1. Identify the Magnitudes and Angle: Determine the magnitudes of vectors A and B and the angle θ between them.
2. Apply the Magnitude Formula: Use the magnitude formula to find R.
3. Determine the Direction: Calculate φ using the direction formula to understand how R aligns with vector A.
Example
If A = 5 units, B = 7 units, and θ = 60 degrees:
- R = √(5² + 7² + 2*5*7*cos(60°))
- Calculate φ using tan(φ) = (7 sin(60°)) / (5 + 7 cos(60°))
This process provides the resultant vector's magnitude and direction, allowing for a comprehensive understanding of vector addition in physics and engineering applications.
When dealing with two vectors, A and B, we can determine the resultant vector by considering both their magnitudes and the angle between them.
Magnitude of the Resultant Vector
To find the magnitude of the resultant vector (R), we use the formula:
- R = √(A² + B² + 2AB cos(θ))
Here,
- A and B are the magnitudes of the two vectors,
- θ is the angle between them,
- cos(θ) accounts for the direction of the vectors.
Direction of the Resultant Vector
The direction of the resultant vector can be calculated using the tangent function:
- tan(φ) = (B sin(θ)) / (A + B cos(θ))
Where φ is the angle the resultant vector makes with vector A.
Steps to Calculate the Resultant
1. Identify the Magnitudes and Angle: Determine the magnitudes of vectors A and B and the angle θ between them.
2. Apply the Magnitude Formula: Use the magnitude formula to find R.
3. Determine the Direction: Calculate φ using the direction formula to understand how R aligns with vector A.
Example
If A = 5 units, B = 7 units, and θ = 60 degrees:
- R = √(5² + 7² + 2*5*7*cos(60°))
- Calculate φ using tan(φ) = (7 sin(60°)) / (5 + 7 cos(60°))
This process provides the resultant vector's magnitude and direction, allowing for a comprehensive understanding of vector addition in physics and engineering applications.
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Find the magnitude and direction of the resultant of two vectors of A vector and B vector in terms of their magnitudes and angle theta between them.?
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Find the magnitude and direction of the resultant of two vectors of A vector and B vector in terms of their magnitudes and angle theta between them.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find the magnitude and direction of the resultant of two vectors of A vector and B vector in terms of their magnitudes and angle theta between them.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the magnitude and direction of the resultant of two vectors of A vector and B vector in terms of their magnitudes and angle theta between them.?.
Find the magnitude and direction of the resultant of two vectors of A vector and B vector in terms of their magnitudes and angle theta between them.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find the magnitude and direction of the resultant of two vectors of A vector and B vector in terms of their magnitudes and angle theta between them.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the magnitude and direction of the resultant of two vectors of A vector and B vector in terms of their magnitudes and angle theta between them.?.
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