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When two vectors in the same direction are added, the magnitude of resulting vector is equal to _______
- a)Sum of magnitudes of the vectors
- b)Difference of magnitudes of the vectors
- c)Product of magnitudes of the vectors
- d)Sum of the roots of magnitudes of the vectors
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
When two vectors in the same direction are added, the magnitude of res...
When two vectors are added, the resulting vector is called the resultant vector. The magnitude of the resultant vector is determined by the magnitudes of the two vectors being added.
Explanation:
- Definition of Magnitude: The magnitude of a vector represents its size or length. It is a scalar value and is always positive.
- Addition of Vectors: When two vectors are added, their magnitudes are combined to obtain the magnitude of the resultant vector. The direction of the resultant vector is determined by the directions of the two vectors being added.
- Same Direction: When two vectors are in the same direction, it means they have the same angle with respect to a reference axis. In this case, the magnitude of the resultant vector is equal to the sum of the magnitudes of the individual vectors.
- Example: Let's consider two vectors A and B, both having a magnitude of 5 units and are in the same direction. When these vectors are added, the magnitude of the resultant vector is 5 + 5 = 10 units.
- Geometric Representation: Geometrically, when two vectors are in the same direction, they lie on the same line. Adding them simply extends the line and increases its length. The magnitude of the resultant vector represents the length of the extended line.
- Algebraic Representation: Algebraically, if A and B are the magnitudes of two vectors in the same direction, the magnitude of the resultant vector R can be represented as R = A + B.
Therefore, the correct answer is option 'A': The magnitude of the resulting vector is equal to the sum of the magnitudes of the vectors.
Explanation:
- Definition of Magnitude: The magnitude of a vector represents its size or length. It is a scalar value and is always positive.
- Addition of Vectors: When two vectors are added, their magnitudes are combined to obtain the magnitude of the resultant vector. The direction of the resultant vector is determined by the directions of the two vectors being added.
- Same Direction: When two vectors are in the same direction, it means they have the same angle with respect to a reference axis. In this case, the magnitude of the resultant vector is equal to the sum of the magnitudes of the individual vectors.
- Example: Let's consider two vectors A and B, both having a magnitude of 5 units and are in the same direction. When these vectors are added, the magnitude of the resultant vector is 5 + 5 = 10 units.
- Geometric Representation: Geometrically, when two vectors are in the same direction, they lie on the same line. Adding them simply extends the line and increases its length. The magnitude of the resultant vector represents the length of the extended line.
- Algebraic Representation: Algebraically, if A and B are the magnitudes of two vectors in the same direction, the magnitude of the resultant vector R can be represented as R = A + B.
Therefore, the correct answer is option 'A': The magnitude of the resulting vector is equal to the sum of the magnitudes of the vectors.
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Community Answer
When two vectors in the same direction are added, the magnitude of res...
Consider the graphical representation of these two vectors. When one vector is added to the other in the same direction, the lengths will be added. The resultant vector will bear the resultant length. Length is the magnitude of the vector. Hence the magnitudes add to give the magnitude of the resultant vector.
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When two vectors in the same direction are added, the magnitude of resulting vector is equal to _______a)Sum of magnitudes of the vectorsb)Difference of magnitudes of the vectorsc)Product of magnitudes of the vectorsd)Sum of the roots of magnitudes of the vectorsCorrect answer is option 'A'. Can you explain this answer?
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