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The resultant of two vectors A and vector B has magnitude 2N. The magnitude of vector A is 2√3N and it makes an angle 30 degree with the resultant. Find the magnitude of vector B(in Newton).?
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The resultant of two vectors A and vector B has magnitude 2N. The magn...
Given:
Magnitude of vector A = 2√3N
Angle between vector A and resultant = 30 degrees
Magnitude of resultant = 2N
To find:
Magnitude of vector B
Solution:
Let the angle between vector B and the resultant be θ.
Using the law of cosines, we have:
Magnitude of vector A = √[(magnitude of resultant)^2 + (magnitude of vector B)^2 - 2(magnitude of resultant)(magnitude of vector B)cosθ]
Substituting the given values, we get:
2√3N = √[(2N)^2 + (magnitude of vector B)^2 - 4N(magnitude of vector B)cosθ]
Simplifying, we get:
12 = 4 + (magnitude of vector B)^2 - 4(magnitude of vector B)cosθ
8 = (magnitude of vector B)^2 - 4(magnitude of vector B)cosθ
2 = (magnitude of vector B)(2cosθ - (magnitude of vector B))
Now, using the law of sines, we have:
(sinθ)/(magnitude of resultant) = (sin(30))/2
sinθ = 1
θ = 90 degrees
Substituting θ = 90 degrees, we get:
2 = (magnitude of vector B)(2cos90 - (magnitude of vector B))
2 = (magnitude of vector B)(-magnitude of vector B)
2 = -(magnitude of vector B)^2
Magnitude of vector B = √(-2) (Note that the magnitude of vector B cannot be negative, hence there is no real solution)
Answer:
There is no real solution for the magnitude of vector B.
Magnitude of vector A = 2√3N
Angle between vector A and resultant = 30 degrees
Magnitude of resultant = 2N
To find:
Magnitude of vector B
Solution:
Let the angle between vector B and the resultant be θ.
Using the law of cosines, we have:
Magnitude of vector A = √[(magnitude of resultant)^2 + (magnitude of vector B)^2 - 2(magnitude of resultant)(magnitude of vector B)cosθ]
Substituting the given values, we get:
2√3N = √[(2N)^2 + (magnitude of vector B)^2 - 4N(magnitude of vector B)cosθ]
Simplifying, we get:
12 = 4 + (magnitude of vector B)^2 - 4(magnitude of vector B)cosθ
8 = (magnitude of vector B)^2 - 4(magnitude of vector B)cosθ
2 = (magnitude of vector B)(2cosθ - (magnitude of vector B))
Now, using the law of sines, we have:
(sinθ)/(magnitude of resultant) = (sin(30))/2
sinθ = 1
θ = 90 degrees
Substituting θ = 90 degrees, we get:
2 = (magnitude of vector B)(2cos90 - (magnitude of vector B))
2 = (magnitude of vector B)(-magnitude of vector B)
2 = -(magnitude of vector B)^2
Magnitude of vector B = √(-2) (Note that the magnitude of vector B cannot be negative, hence there is no real solution)
Answer:
There is no real solution for the magnitude of vector B.
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The resultant of two vectors A and vector B has magnitude 2N. The magnitude of vector A is 2√3N and it makes an angle 30 degree with the resultant. Find the magnitude of vector B(in Newton).?
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The resultant of two vectors A and vector B has magnitude 2N. The magnitude of vector A is 2√3N and it makes an angle 30 degree with the resultant. Find the magnitude of vector B(in Newton).? 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 resultant of two vectors A and vector B has magnitude 2N. The magnitude of vector A is 2√3N and it makes an angle 30 degree with the resultant. Find the magnitude of vector B(in Newton).? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The resultant of two vectors A and vector B has magnitude 2N. The magnitude of vector A is 2√3N and it makes an angle 30 degree with the resultant. Find the magnitude of vector B(in Newton).?.
The resultant of two vectors A and vector B has magnitude 2N. The magnitude of vector A is 2√3N and it makes an angle 30 degree with the resultant. Find the magnitude of vector B(in Newton).? 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 resultant of two vectors A and vector B has magnitude 2N. The magnitude of vector A is 2√3N and it makes an angle 30 degree with the resultant. Find the magnitude of vector B(in Newton).? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The resultant of two vectors A and vector B has magnitude 2N. The magnitude of vector A is 2√3N and it makes an angle 30 degree with the resultant. Find the magnitude of vector B(in Newton).?.
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