Which of the following two statements is more appropriate?
(a) Two velocities are added using triangle rule because velocity is vector quantity.
(b) Velocity is a vector quantity because two velocities are added using triangle rule.

Answer

To determine which of the two statements is more appropriate, let's analyze each statement step by step.

### Step 1: Understanding the Statements
- **Statement (a)**: "Two velocities are added using triangle rule because velocity is a vector quantity."
- **Statement (b)**: "Velocity is a vector quantity because two velocities are added using triangle rule."

### Step 2: Analyzing Statement (a)
- This statement claims that the reason we can add two velocities using the triangle rule is that velocity is a vector quantity.
- This is true because the triangle law of vector addition applies to vector quantities, including velocity. Vectors have both magnitude and direction, which allows for this type of addition.

### Step 3: Analyzing Statement (b)
- This statement claims that the reason velocity is a vector quantity is that we can add two velocities using the triangle rule.
- This is misleading because the definition of a vector quantity is not dependent on how we can add it. A vector is defined by its properties (magnitude and direction), and the ability to add it using the triangle rule is a consequence of it being a vector, not the other way around.

### Step 4: Conclusion
- Based on the analysis, **Statement (a)** is correct because it accurately reflects the relationship between vector quantities and the triangle rule of addition.
- **Statement (b)** is incorrect because it incorrectly implies that the property of being a vector is derived from the ability to add it using the triangle rule.

### Final Answer
The more appropriate statement is (a): "Two velocities are added using triangle rule because velocity is a vector quantity."

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