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Asserion: Magnitude of the resultant of ...

Asserion: Magnitude of the resultant of two vectors may be less than the magnitude of either vector.
Reason: The resultant of two vectors is obtained by means of law of parallelogram of Vectors.

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To analyze the assertion and reason provided in the question, we will break it down step by step. ### Step 1: Understanding the Assertion The assertion states that "the magnitude of the resultant of two vectors may be less than the magnitude of either vector." - **Explanation**: This means that when you add two vectors, the resultant vector (the vector that represents the combined effect of the two vectors) can sometimes have a smaller magnitude than either of the individual vectors. ### Step 2: Analyzing with Examples To understand this better, let's consider two vectors, A and B. - **Case 1**: If both vectors are in the same direction, the resultant vector (C = A + B) will be greater than both A and B. - **Case 2**: If the two vectors are in opposite directions, the resultant can be less than the magnitude of either vector. For example, if A = 5 units to the right and B = 3 units to the left, the resultant C = A - B = 5 - 3 = 2 units to the right, which is less than the magnitude of A. ### Step 3: Conclusion on the Assertion From our analysis, we can conclude that the assertion is true because there are scenarios (like Case 2) where the resultant can indeed be less than either of the vectors. ### Step 4: Understanding the Reason The reason states that "the resultant of two vectors is obtained by means of the law of parallelogram of vectors." - **Explanation**: The law of parallelogram states that if two vectors are represented as two sides of a parallelogram, then the diagonal of the parallelogram represents the resultant vector. ### Step 5: Analyzing the Reason While the reason is correct in stating how to find the resultant vector, it does not specifically explain why the resultant can be less than either vector. ### Step 6: Conclusion on the Reason Thus, the reason is true, but it does not provide an explanation for the assertion. ### Final Conclusion Both the assertion and the reason are true, but the reason does not explain the assertion. ### Summary - **Assertion**: True - **Reason**: True, but does not explain the assertion.

To analyze the assertion and reason provided in the question, we will break it down step by step. ### Step 1: Understanding the Assertion The assertion states that "the magnitude of the resultant of two vectors may be less than the magnitude of either vector." - **Explanation**: This means that when you add two vectors, the resultant vector (the vector that represents the combined effect of the two vectors) can sometimes have a smaller magnitude than either of the individual vectors. ### Step 2: Analyzing with Examples ...
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