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Assertion: The minimum number of non-cop...

Assertion: The minimum number of non-coplanar Vectors whose sum can be zero, is four
Reason: The resultant of two vectors of unequal magnitude can be zero.

A

If both assertion and reason are true and reason is the correct explanation of assertion.

B

If both assertion and reason are true but reason is not the correct explanation of assertion

C

If assertion is true but reason is false.

D

If both aseertion and reason are false.

Text Solution

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The correct Answer is:
To solve the given problem, we need to analyze the assertion and the reason provided. ### Step 1: Analyze the Assertion The assertion states that the minimum number of non-coplanar vectors whose sum can be zero is four. - **Understanding Non-Coplanar Vectors**: Non-coplanar vectors are vectors that do not lie in the same plane. For the sum of vectors to be zero, they must balance each other out in three-dimensional space. - **Example with Four Vectors**: Consider four vectors A, B, C, and D. If we arrange them in such a way that they form a closed tetrahedron, their vector sum can be zero. For instance: - Vector A can point in one direction. - Vector B can point in a different direction. - Vector C can point in a third direction. - Vector D can be directed such that it balances out the other three vectors. Thus, the assertion is **true**. ### Step 2: Analyze the Reason The reason states that the resultant of two vectors of unequal magnitude can be zero. - **Understanding Resultant of Two Vectors**: The resultant of two vectors can only be zero if they are equal in magnitude and opposite in direction. If two vectors have unequal magnitudes, their resultant cannot be zero. - **Conclusion on Reason**: Since the reason provided is incorrect, it is **false**. ### Final Conclusion - The assertion is true, and the reason is false. Therefore, the correct answer is that the assertion is true, but the reason is false. ### Summary of the Solution - **Assertion**: True (Minimum number of non-coplanar vectors whose sum can be zero is four). - **Reason**: False (The resultant of two vectors of unequal magnitude cannot be zero).

To solve the given problem, we need to analyze the assertion and the reason provided. ### Step 1: Analyze the Assertion The assertion states that the minimum number of non-coplanar vectors whose sum can be zero is four. - **Understanding Non-Coplanar Vectors**: Non-coplanar vectors are vectors that do not lie in the same plane. For the sum of vectors to be zero, they must balance each other out in three-dimensional space. - **Example with Four Vectors**: Consider four vectors A, B, C, and D. If we arrange them in such a way that they form a closed tetrahedron, their vector sum can be zero. For instance: ...
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  12. Assertion: The scalar product of two vectors can be zero Reason: If...

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  13. Assertion: If vec(A).vec(B)= vec(B).vec(C ), then vec(A) may not alway...

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  14. Assertion: If theta be the angle between vec(A) and vec(B), then tan...

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