State with reasons, whether the following algebraic operations with scalar and vector physical quantities are meaningful:
(i) Adding any two scalars (ii) Adding a scalar to a vector of the same dimensions
(iii) Multiplying any vector by any scalar (iv) Multiplying any two scalars
(v) Adding any two vectors

Explanation

To determine whether the given algebraic operations with scalar and vector physical quantities are meaningful, we will analyze each operation step by step.

### Step-by-Step Solution:

1. **Adding any two scalars:**
- **Explanation:** Adding two scalars is meaningful as long as they represent the same physical quantity. Scalars are quantities that have magnitude only and no direction. For example, adding 5 kg to 3 kg gives 8 kg, which is valid.
- **Conclusion:** **Meaningful** if they have the same dimension.

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