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The angle between two vector of equal magnitude is 120* .Prove that the magnitude of their resultant either of the .?
Most Upvoted Answer
The angle between two vector of equal magnitude is 120* .Prove that th...
Proof:
Let us consider two equal magnitude vectors A and B.
Step 1: Draw a diagram
A diagram can help in visualizing the problem. Draw two vectors of equal magnitude, A and B, making an angle of 120 degrees between them.
Step 2: Draw a parallelogram
Draw a parallelogram using A and B as two adjacent sides.
Step 3: Draw the diagonal
Draw the diagonal of the parallelogram that passes through the point where A and B meet. This diagonal represents the resultant vector, R.
Step 4: Use the law of cosines
Apply the law of cosines to the triangle formed by A, B, and R.
cos(120) = (A^2 + B^2 - R^2) / (2AB)
Since A and B have equal magnitudes, we can simplify this equation to:
cos(120) = (2A^2 - R^2) / (2A^2)
Simplify further to get:
R^2 = 4A^2 - 4A^2cos(120)
R^2 = 4A^2 - 4A^2(-1/2)
R^2 = 4A^2 + 2A^2
R^2 = 6A^2
Step 5: Conclusion
We can see that the magnitude of the resultant vector, R, is equal to the square root of 6 times the magnitude of either A or B. Therefore, the magnitude of the resultant vector is always greater than the magnitude of either A or B.
Let us consider two equal magnitude vectors A and B.
Step 1: Draw a diagram
A diagram can help in visualizing the problem. Draw two vectors of equal magnitude, A and B, making an angle of 120 degrees between them.
Step 2: Draw a parallelogram
Draw a parallelogram using A and B as two adjacent sides.
Step 3: Draw the diagonal
Draw the diagonal of the parallelogram that passes through the point where A and B meet. This diagonal represents the resultant vector, R.
Step 4: Use the law of cosines
Apply the law of cosines to the triangle formed by A, B, and R.
cos(120) = (A^2 + B^2 - R^2) / (2AB)
Since A and B have equal magnitudes, we can simplify this equation to:
cos(120) = (2A^2 - R^2) / (2A^2)
Simplify further to get:
R^2 = 4A^2 - 4A^2cos(120)
R^2 = 4A^2 - 4A^2(-1/2)
R^2 = 4A^2 + 2A^2
R^2 = 6A^2
Step 5: Conclusion
We can see that the magnitude of the resultant vector, R, is equal to the square root of 6 times the magnitude of either A or B. Therefore, the magnitude of the resultant vector is always greater than the magnitude of either A or B.
Community Answer
The angle between two vector of equal magnitude is 120* .Prove that th...
Let the 2 vectors be A and B and their resultant be R. To prove :- A=B=R. . R^2 = A^2 + B^2 + 2ABCostheta . A^2 = B^2 = R^2 , R^2 = R^2 + R^2 + 2R^2 (Costheta) . R^2 = 2R^2 + 2R^2 (Costheta) Cos theta = (R^2 - 2R^2) / 2R^2 = (-R^2) / 2R^2 Cos theta = -1/2 theta = 120 degrees. . hence proved.
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The angle between two vector of equal magnitude is 120* .Prove that the magnitude of their resultant either of the .?
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The angle between two vector of equal magnitude is 120* .Prove that the magnitude of their resultant either of the .? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The angle between two vector of equal magnitude is 120* .Prove that the magnitude of their resultant either of the .? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The angle between two vector of equal magnitude is 120* .Prove that the magnitude of their resultant either of the .?.
The angle between two vector of equal magnitude is 120* .Prove that the magnitude of their resultant either of the .? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The angle between two vector of equal magnitude is 120* .Prove that the magnitude of their resultant either of the .? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The angle between two vector of equal magnitude is 120* .Prove that the magnitude of their resultant either of the .?.
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