In the following questions a statement of assertion (A) is followed by a statement of reason ( R).
A: Angular displacement is vector quntity only for small values .
R: The direction of angular displacement is perpendicular to plane of rotation of object .

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 question regarding the assertion and reason statements about angular displacement, we will analyze both statements step by step.

### Step 1: Understanding Angular Displacement
- **Assertion (A)** states that "Angular displacement is a vector quantity only for small values."
- Angular displacement is defined as the angle through which an object has rotated about a specific axis in a given time. It is indeed a vector quantity because it has both magnitude and direction.

### Step 2: Analyzing the Assertion
- For small angular displacements, the path taken by the object can be approximated as a straight line, making it easier to define a clear direction for the vector.
- However, for larger angular displacements (like a full rotation), the direction of the vector can become ambiguous since the object returns to its starting position, leading to a net angular displacement of zero.

### Step 3: Understanding the Reason
- **Reason (R)** states that "The direction of angular displacement is perpendicular to the plane of rotation of the object."
- This statement is true. The direction of the angular displacement vector is given by the right-hand rule, which states that if you curl the fingers of your right hand in the direction of rotation, your thumb points in the direction of the angular displacement vector.

### Step 4: Evaluating the Truth of Each Statement
- Both the assertion and the reason are true:
- The assertion correctly identifies that angular displacement is a vector quantity, particularly for small values.
- The reason correctly describes the direction of the angular displacement vector.

### Step 5: Determining the Relationship Between Assertion and Reason
- While both statements are true, the reason provided does not adequately explain why the assertion is true. The assertion focuses on the behavior of angular displacement for small values, while the reason discusses the directionality of the vector without addressing the context of small versus large displacements.

### Conclusion
- Therefore, the conclusion is that both the assertion and reason are true, but the reason is not the correct explanation for the assertion.

### Final Answer
- **Assertion (A)**: True
- **Reason (R)**: True
- **Conclusion**: The reason is not the correct explanation of the assertion.