Assertion: Adding a scalar to a vector of the same dimensions is a meanigful algeraic operation.
Reason: The displacement can be added with distance.

Explanation

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

### Step 1: Analyze the Assertion
The assertion states: "Adding a scalar to a vector of the same dimensions is a meaningful algebraic operation."

- A scalar is a quantity that has magnitude only, while a vector has both magnitude and direction.
- In mathematics and physics, adding a scalar to a vector is not a valid operation because they are fundamentally different types of quantities. Therefore, the assertion is **false**.

### Step 2: Analyze the Reason
The reason states: "The displacement can be added with distance."

- Displacement is a vector quantity, which means it has both magnitude and direction.
- Distance, on the other hand, is a scalar quantity, which only has magnitude and no direction.
- Since a vector cannot be added to a scalar, it follows that displacement cannot be added to distance. Therefore, this reason is also **false**.

### Conclusion
Both the assertion and the reason are incorrect.

Thus, the final answer is:
- **Assertion is false.**
- **Reason is false.**