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Given that vectorA vectorB vectorC =0.out of three vectors two are equal in magnitude and the magnitude of third vector is root2 times that of the two having equal magnitude.Then what's the angle between the vectors?
Most Upvoted Answer
Given that vectorA vectorB vectorC =0.out of three vectors two are eq...
Given Information:
We are given three vectors, vector A, vector B, and vector C, such that vector A + vector B + vector C = 0. It is also mentioned that two of the vectors have equal magnitudes, and the magnitude of the third vector is √2 times that of the two vectors with equal magnitudes.
To Find:
We need to determine the angle between the vectors.
Solution:
Step 1: Analyzing the Given Information
Let's denote the magnitude of the vectors with equal magnitudes as 'x'. Since the magnitude of the third vector is √2 times that of the vectors with equal magnitudes, its magnitude will be √2x.
Step 2: Vector Addition
Given that vector A + vector B + vector C = 0, we can rewrite it as:
vector A + vector B = -vector C
Step 3: Magnitude of Vector C
The magnitude of a vector is given by the formula:
| vector | = √(vector x² + vector y² + vector z²)
Since vector C = -(vector A + vector B), we can substitute this in the magnitude formula:
| vector C | = √((vector A + vector B) x² + (vector A + vector B) y² + (vector A + vector B) z²)
Step 4: Expanding and Simplifying
Expanding the above equation, we get:
| vector C | = √(vector A x² + 2(vector A)(vector B) + vector B x² + vector A y² + 2(vector A)(vector B) + vector B y² + vector A z² + 2(vector A)(vector B) + vector B z²)
Since vector A and vector B have equal magnitudes 'x', this equation simplifies to:
| vector C | = √(2x² + 2x² + 2x²) = √(6x²)
Similarly, we can find the magnitude of vector C using the given information:
| vector C | = √(√2x²) = √2x
Step 5: Equating and Solving for x
Since the magnitude of vector C can be calculated in two different ways, we can equate the two expressions:
√(6x²) = √2x
Squaring both sides of the equation, we get:
6x² = 2x²
Simplifying, we find:
4x² = 0
Since the magnitude of a vector cannot be zero, this equation has no solution.
Step 6: Conclusion
The equation has no solution, which means it is not possible to have two vectors with equal magnitudes and a third vector with a magnitude √2 times that of the other two vectors while satisfying the condition vector A + vector B + vector C = 0.
Therefore, the given scenario is not possible, and we cannot determine the angle between the vectors.
We are given three vectors, vector A, vector B, and vector C, such that vector A + vector B + vector C = 0. It is also mentioned that two of the vectors have equal magnitudes, and the magnitude of the third vector is √2 times that of the two vectors with equal magnitudes.
To Find:
We need to determine the angle between the vectors.
Solution:
Step 1: Analyzing the Given Information
Let's denote the magnitude of the vectors with equal magnitudes as 'x'. Since the magnitude of the third vector is √2 times that of the vectors with equal magnitudes, its magnitude will be √2x.
Step 2: Vector Addition
Given that vector A + vector B + vector C = 0, we can rewrite it as:
vector A + vector B = -vector C
Step 3: Magnitude of Vector C
The magnitude of a vector is given by the formula:
| vector | = √(vector x² + vector y² + vector z²)
Since vector C = -(vector A + vector B), we can substitute this in the magnitude formula:
| vector C | = √((vector A + vector B) x² + (vector A + vector B) y² + (vector A + vector B) z²)
Step 4: Expanding and Simplifying
Expanding the above equation, we get:
| vector C | = √(vector A x² + 2(vector A)(vector B) + vector B x² + vector A y² + 2(vector A)(vector B) + vector B y² + vector A z² + 2(vector A)(vector B) + vector B z²)
Since vector A and vector B have equal magnitudes 'x', this equation simplifies to:
| vector C | = √(2x² + 2x² + 2x²) = √(6x²)
Similarly, we can find the magnitude of vector C using the given information:
| vector C | = √(√2x²) = √2x
Step 5: Equating and Solving for x
Since the magnitude of vector C can be calculated in two different ways, we can equate the two expressions:
√(6x²) = √2x
Squaring both sides of the equation, we get:
6x² = 2x²
Simplifying, we find:
4x² = 0
Since the magnitude of a vector cannot be zero, this equation has no solution.
Step 6: Conclusion
The equation has no solution, which means it is not possible to have two vectors with equal magnitudes and a third vector with a magnitude √2 times that of the other two vectors while satisfying the condition vector A + vector B + vector C = 0.
Therefore, the given scenario is not possible, and we cannot determine the angle between the vectors.
Community Answer
Given that vectorA vectorB vectorC =0.out of three vectors two are eq...
Angle btw A and B is 60 and A and C is150
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Given that vectorA vectorB vectorC =0.out of three vectors two are equal in magnitude and the magnitude of third vector is root2 times that of the two having equal magnitude.Then what's the angle between the vectors?
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Given that vectorA vectorB vectorC =0.out of three vectors two are equal in magnitude and the magnitude of third vector is root2 times that of the two having equal magnitude.Then what's the angle between the vectors? 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 Given that vectorA vectorB vectorC =0.out of three vectors two are equal in magnitude and the magnitude of third vector is root2 times that of the two having equal magnitude.Then what's the angle between the vectors? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given that vectorA vectorB vectorC =0.out of three vectors two are equal in magnitude and the magnitude of third vector is root2 times that of the two having equal magnitude.Then what's the angle between the vectors?.
Given that vectorA vectorB vectorC =0.out of three vectors two are equal in magnitude and the magnitude of third vector is root2 times that of the two having equal magnitude.Then what's the angle between the vectors? 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 Given that vectorA vectorB vectorC =0.out of three vectors two are equal in magnitude and the magnitude of third vector is root2 times that of the two having equal magnitude.Then what's the angle between the vectors? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given that vectorA vectorB vectorC =0.out of three vectors two are equal in magnitude and the magnitude of third vector is root2 times that of the two having equal magnitude.Then what's the angle between the vectors?.
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