Assertion : Particle A is moving Eastwards and particle B Northwards with same speed. Then, velocity of A with respect to B is in South-East direction.
Reason : Relative velocity between them is zero as their speeds are same.

Options

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

Explanation

To solve the given question, we will analyze the assertion and reason step by step.

### Step 1: Understand the Motion of Particles A and B
- Particle A is moving Eastwards, which we can represent as a vector \( \vec{V_A} = v \hat{i} \) (where \( v \) is the speed and \( \hat{i} \) is the unit vector in the East direction).
- Particle B is moving Northwards, represented as \( \vec{V_B} = v \hat{j} \) (where \( \hat{j} \) is the unit vector in the North direction).

### Step 2: Calculate the Relative Velocity of A with Respect to B
- The relative velocity of A with respect to B is given by the formula:
\[ \vec{V_{A/B}} = \vec{V_A} - \vec{V_B} \]
- Substituting the values:
\[ \vec{V_{A/B}} = (v \hat{i}) - (v \hat{j}) = v \hat{i} - v \hat{j} \]

### Step 3: Analyze the Resultant Velocity Vector
- The resultant vector \( \vec{V_{A/B}} = v \hat{i} - v \hat{j} \) can be interpreted as having components in the East and South directions.
- To find the direction of this vector, we can visualize it in the Cartesian coordinate system:
- The positive x-direction (East) and the negative y-direction (South) indicate that the resultant vector points towards the South-East.

### Step 4: Conclusion on the Assertion
- The assertion states that the velocity of A with respect to B is in the South-East direction. This is indeed correct based on our calculations.

### Step 5: Analyze the Reason
- The reason states that the relative velocity between them is zero because their speeds are the same. This is incorrect because, although they have the same speed, they are moving in different directions, resulting in a non-zero relative velocity.

### Final Conclusion
- The assertion is true, while the reason is false. Therefore, the correct answer is that the assertion is true, but the reason is false.