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A resultant of two vectors makes 30 with one vector and 45 degree with the other. Find the two vectors if the resultant has the magnitude 15 .?
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Explanation:
Let the two vectors be A and B. Let the resultant be R.
Given, magnitude of R = 15
Let the angle between R and A be θ1 and the angle between R and B be θ2.
Given, θ1 = 30° and θ2 = 45°
We know that the magnitude of the resultant of two vectors is given by:
|R| = √(A² + B² + 2ABcosθ)
where A and B are the magnitudes of the two vectors and θ is the angle between them.
Finding the Magnitudes of A and B:
We can use the above formula to find the magnitudes of A and B.
|R| = √(A² + B² + 2ABcosθ)
Substituting the given values, we get:
15 = √(A² + B² + 2ABcos30°) = √(A² + B² + AB√3)
Squaring both sides, we get:
225 = A² + B² + AB√3
Similarly, using the angle θ2, we get:
225 = A² + B² + AB
Solving these two equations, we get:
A = 5√3 and B = 5
Finding the Direction of A and B:
To find the direction of A and B, we can use the angles θ1 and θ2.
Let the angle between A and the x-axis be α and the angle between B and the x-axis be β.
Using trigonometry, we get:
tanα = (A sinθ1) / (A cosθ1) = √3
tanβ = (B sinθ2) / (B cosθ2) = 1
Therefore, α = 60° and β = 45°.
Hence, the two vectors are A = 5√3 at an angle of 60° with the x-axis and B = 5 at an angle of 45° with the x-axis.
Let the two vectors be A and B. Let the resultant be R.
Given, magnitude of R = 15
Let the angle between R and A be θ1 and the angle between R and B be θ2.
Given, θ1 = 30° and θ2 = 45°
We know that the magnitude of the resultant of two vectors is given by:
|R| = √(A² + B² + 2ABcosθ)
where A and B are the magnitudes of the two vectors and θ is the angle between them.
Finding the Magnitudes of A and B:
We can use the above formula to find the magnitudes of A and B.
|R| = √(A² + B² + 2ABcosθ)
Substituting the given values, we get:
15 = √(A² + B² + 2ABcos30°) = √(A² + B² + AB√3)
Squaring both sides, we get:
225 = A² + B² + AB√3
Similarly, using the angle θ2, we get:
225 = A² + B² + AB
Solving these two equations, we get:
A = 5√3 and B = 5
Finding the Direction of A and B:
To find the direction of A and B, we can use the angles θ1 and θ2.
Let the angle between A and the x-axis be α and the angle between B and the x-axis be β.
Using trigonometry, we get:
tanα = (A sinθ1) / (A cosθ1) = √3
tanβ = (B sinθ2) / (B cosθ2) = 1
Therefore, α = 60° and β = 45°.
Hence, the two vectors are A = 5√3 at an angle of 60° with the x-axis and B = 5 at an angle of 45° with the x-axis.
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A resultant of two vectors makes 30 with one vector and 45 degree with the other. Find the two vectors if the resultant has the magnitude 15 .?
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A resultant of two vectors makes 30 with one vector and 45 degree with the other. Find the two vectors if the resultant has the magnitude 15 .? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A resultant of two vectors makes 30 with one vector and 45 degree with the other. Find the two vectors if the resultant has the magnitude 15 .? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A resultant of two vectors makes 30 with one vector and 45 degree with the other. Find the two vectors if the resultant has the magnitude 15 .?.
A resultant of two vectors makes 30 with one vector and 45 degree with the other. Find the two vectors if the resultant has the magnitude 15 .? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A resultant of two vectors makes 30 with one vector and 45 degree with the other. Find the two vectors if the resultant has the magnitude 15 .? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A resultant of two vectors makes 30 with one vector and 45 degree with the other. Find the two vectors if the resultant has the magnitude 15 .?.
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