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In the following questions a statement o...

In the following questions a statement of assertion (A) is followed by a statement of reason ( R).
A: A vector cannot be divided by other by other vector .
R: A vector can be divided by a scalar .

A

If both Assertion & Reason are true and the reason is the correct explanation of the assertion then mark (1) .

B

If both Assertion & Reason are true but the reason is not the correct explanation of the assertion then mark (2)

C

If Assertion is true statement but Reason is false then mark (3).

D

If both Assertion and Reason are false statements then mark (4) .

Text Solution

AI Generated Solution

The correct Answer is:
To solve the given question, we need to analyze both the assertion (A) and the reason (R) provided. ### Step-by-Step Solution: 1. **Understanding the Assertion (A)**: - The assertion states: "A vector cannot be divided by another vector." - This is true because division of vectors is not defined in vector algebra. We can only perform operations like addition, subtraction, and multiplication (dot and cross product) with vectors. 2. **Understanding the Reason (R)**: - The reason states: "A vector can be divided by a scalar." - This is also true. In vector algebra, we can divide a vector by a scalar to scale the vector. For example, if \( \mathbf{A} \) is a vector and \( k \) is a scalar, then \( \mathbf{A}/k \) is a valid operation which results in a vector that has the same direction as \( \mathbf{A} \) but with a magnitude scaled by \( 1/k \). 3. **Analyzing the Relationship Between A and R**: - Although both the assertion and the reason are true, the reason does not correctly explain the assertion. The assertion is about the inability to divide one vector by another, while the reason discusses the division of a vector by a scalar, which is a different concept. 4. **Conclusion**: - Therefore, we conclude that both the assertion (A) and the reason (R) are true, but the reason is not the correct explanation for the assertion. 5. **Final Answer**: - The correct option is that both A and R are true, but R is not the correct explanation of A.
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