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Three vectors each of magnitude A are acting at a point such that angle between any two vectors is 60 degree. what is the magnitude of their resultant?
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?Three vectors each of magnitude A are acting at a point such that ang...
Given:
Three vectors of magnitude A are acting at a point.
Angle between any two vectors is 60 degrees.
To find:
Magnitude of the resultant vector.
Solution:
To find the magnitude of the resultant vector, we can use the concept of vector addition.
Step 1: Drawing the vectors
Let's draw the three vectors starting from a common point, such as the origin.
Step 2: Finding the resultant vector
To find the resultant vector, we need to add the three vectors together using vector addition.
Step 3: Using vector addition
Since the angle between any two vectors is 60 degrees, and the magnitude of each vector is A, we can form an equilateral triangle using the three vectors.
Step 4: Finding the magnitude of the resultant vector
In an equilateral triangle, the angle between any two sides is 60 degrees. Therefore, the angle between the resultant vector and one of the vectors is also 60 degrees.
Using the law of cosines, we can find the magnitude of the resultant vector:
c^2 = a^2 + b^2 - 2ab * cos(C)
Here, a = A, b = A, and C = 60 degrees.
c^2 = A^2 + A^2 - 2(A)(A) * cos(60)
c^2 = 2A^2 - 2(A)(A)(1/2)
c^2 = 2A^2 - A^2
c^2 = A^2
Taking the square root of both sides, we get:
c = A
Therefore, the magnitude of the resultant vector is A.
Conclusion:
The magnitude of the resultant vector is equal to the magnitude of each individual vector, which is A.
Community Answer
?Three vectors each of magnitude A are acting at a point such that ang...
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?Three vectors each of magnitude A are acting at a point such that angle between any two vectors is 60 degree. what is the magnitude of their resultant?
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?Three vectors each of magnitude A are acting at a point such that angle between any two vectors is 60 degree. what is the magnitude of their resultant? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about ?Three vectors each of magnitude A are acting at a point such that angle between any two vectors is 60 degree. what is the magnitude of their resultant? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ?Three vectors each of magnitude A are acting at a point such that angle between any two vectors is 60 degree. what is the magnitude of their resultant?.
?Three vectors each of magnitude A are acting at a point such that angle between any two vectors is 60 degree. what is the magnitude of their resultant? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about ?Three vectors each of magnitude A are acting at a point such that angle between any two vectors is 60 degree. what is the magnitude of their resultant? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ?Three vectors each of magnitude A are acting at a point such that angle between any two vectors is 60 degree. what is the magnitude of their resultant?.
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