Assertion - Component of A along B is equal to component of B along A.
Reason value of component is always less then the magnitude of vector .

Options

A. If both Assetion and Reason are correct but Reason is the correct explanation of Assertion.
B. If both Assetion and Reason are correct but Reason is not the correct explanation of Assertion.
C. If Asserion is true but Reason is false
D. If Asserion is false but Reason is true

Answer

To solve the question, we need to analyze both the assertion and the reason provided.

### Step 1: Understand the Assertion
The assertion states that the component of vector A along vector B is equal to the component of vector B along vector A.

- The component of vector A along vector B is given by the formula:
\[ A_{B} = \frac{A \cdot B}{|B|} \]
where \( A \cdot B \) is the dot product of vectors A and B, and \( |B| \) is the magnitude of vector B.

- Similarly, the component of vector B along vector A is given by:
\[ B_{A} = \frac{B \cdot A}{|A|} \]

- These two components are generally not equal unless A and B are in the same direction or have the same magnitude. Therefore, the assertion is **false**.

### Step 2: Understand the Reason
The reason states that the value of a component is always less than the magnitude of the vector.

- This is true because the component of a vector is a projection of that vector in a specific direction. By definition, the magnitude of a vector is the longest possible length of that vector, while the component represents only a part of that vector in a particular direction.

- Mathematically, for any vector \( V \):
\[ |V| \geq |V_{B}| \]
where \( |V_{B}| \) is the component of vector V along vector B.

### Conclusion
- The assertion is **false**.
- The reason is **true**.

Thus, the correct answer is that the assertion is false, but the reason is true.

### Final Answer
Assertion is false, Reason is true.

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