Class 11 Exam > Class 11 Questions > Vectors can be added bya)adding the magnitude...
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Vectors can be added by
- a)adding the magnitudes of the vectors
- b)vector addition
- c)translating the two vectors
- d)adding the angles of the vectors
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Vectors can be added bya)adding the magnitudes of the vectorsb)vector ...
Explanation:Vector addition is the operation of adding two or more vectors together into a vector sum. The so-called parallelogram law gives the rule for vector addition of two or more vectors. For two vectors, the vector sum is obtained by placing them head to tail and drawing the vector from the free tail to the free head.
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Vectors can be added bya)adding the magnitudes of the vectorsb)vector ...
Vector Addition:
Vectors can be added through vector addition, which involves breaking down each vector into its horizontal and vertical components and then adding these components separately. The resulting vector will have a magnitude and direction that is the sum of the original vectors.
Process of Vector Addition:
- Resolve each vector into horizontal and vertical components.
- Add the horizontal components of the vectors together.
- Add the vertical components of the vectors together.
- Use the Pythagorean theorem and trigonometric functions to find the magnitude and direction of the resulting vector.
- The resulting vector is the sum of the original vectors.
Example:
Consider two vectors A and B. Vector A has a magnitude of 5 units at an angle of 30 degrees above the horizontal, and vector B has a magnitude of 3 units at an angle of 60 degrees below the horizontal. To find the sum of these vectors, you would:
1. Resolve vector A into horizontal and vertical components.
2. Resolve vector B into horizontal and vertical components.
3. Add the horizontal components of A and B together.
4. Add the vertical components of A and B together.
5. Use trigonometry to find the magnitude and direction of the resulting vector.
Conclusion:
Vector addition is the most common method of adding vectors and allows for the determination of the resultant vector from multiple vectors. This method is essential in physics, engineering, and mathematics for calculating forces, velocities, and displacements.
Vectors can be added through vector addition, which involves breaking down each vector into its horizontal and vertical components and then adding these components separately. The resulting vector will have a magnitude and direction that is the sum of the original vectors.
Process of Vector Addition:
- Resolve each vector into horizontal and vertical components.
- Add the horizontal components of the vectors together.
- Add the vertical components of the vectors together.
- Use the Pythagorean theorem and trigonometric functions to find the magnitude and direction of the resulting vector.
- The resulting vector is the sum of the original vectors.
Example:
Consider two vectors A and B. Vector A has a magnitude of 5 units at an angle of 30 degrees above the horizontal, and vector B has a magnitude of 3 units at an angle of 60 degrees below the horizontal. To find the sum of these vectors, you would:
1. Resolve vector A into horizontal and vertical components.
2. Resolve vector B into horizontal and vertical components.
3. Add the horizontal components of A and B together.
4. Add the vertical components of A and B together.
5. Use trigonometry to find the magnitude and direction of the resulting vector.
Conclusion:
Vector addition is the most common method of adding vectors and allows for the determination of the resultant vector from multiple vectors. This method is essential in physics, engineering, and mathematics for calculating forces, velocities, and displacements.
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