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 .

Options

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) .

Answer

To solve the given question, we need to analyze the assertion (A) and the reason (R) provided.

### Step 1: Analyze the Assertion (A)
The assertion states: "A vector cannot be divided by another vector."

- **Explanation**: This statement is true. In vector mathematics, division of one vector by another vector is not defined. Instead, we can perform operations like addition, subtraction, and scalar multiplication. To combine vectors, we often use the dot product or cross product, but direct division is not permissible.

### Step 2: Analyze the Reason (R)
The reason states: "A vector can be divided by a scalar."

- **Explanation**: This statement is also true. A vector can indeed be divided by a scalar. When you divide a vector by a scalar, you are essentially scaling the vector. For example, if you have a vector \( \mathbf{A} = 2\hat{i} + 3\hat{j} \) and you divide it by a scalar \( 2 \), the result is \( \frac{1}{2}(2\hat{i} + 3\hat{j}) = \hat{i} + \frac{3}{2}\hat{j} \). This operation is valid and results in a new vector.

### Step 3: Determine the Relationship Between A and R
Now, we need to determine if the reason (R) correctly explains the assertion (A).

- **Explanation**: While both statements are true, the reason does not explain the assertion. The assertion is about the impossibility of dividing vectors, while the reason discusses the division of vectors by scalars, which is a different concept. Therefore, while both are true, they are not related.

### Conclusion
Based on the analysis:
- Both the assertion (A) and the reason (R) are true.
- However, the reason (R) does not correctly explain the assertion (A).

Thus, the correct answer is that both the assertion and reason are true, but the reason is not the correct explanation for the assertion.

### Final Answer
Both assertion and reason are true, but the reason is not the correct explanation for the assertion.

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