Choose the correct statement

Options

A. Temperature is a scalar but temperature gradient is a vector
B. Velocity of a body is a vector but velocity of light is a scalar
C. Electric intensity and Electric current density are vectors
D. all the above

Answer

To solve the question "Choose the correct statement," we will analyze each statement provided in the question step by step.

### Step 1: Analyze Statement 1
**Statement 1:** Temperature is a scalar quantity.

- **Explanation:** Temperature is a measure of thermal energy and is defined by a numerical value without any direction. Thus, it is classified as a scalar quantity. The temperature gradient, however, is a vector quantity because it indicates the direction of change in temperature.

**Conclusion:** Statement 1 is correct.

### Step 2: Analyze Statement 2
**Statement 2:** Velocity of a body is a vector but velocity of light is a scalar.

- **Explanation:** Velocity is defined as the rate of change of displacement and includes both magnitude and direction, making it a vector quantity. However, the velocity of light is often treated as a constant (approximately \(3 \times 10^8\) m/s in a vacuum) and does not follow the same rules of vector addition as other velocities. This is due to the principles of relativity, which state that the speed of light is invariant in all inertial frames of reference.

**Conclusion:** Statement 2 is misleading. The velocity of light is a vector quantity, but it does not behave like other velocities under certain conditions.

### Step 3: Analyze Statement 3
**Statement 3:** Electric intensity and electric current density are vector quantities.

- **Explanation:** Electric intensity (or electric field) is represented by the vector \( \mathbf{E} \), which has both magnitude and direction. Similarly, electric current density \( \mathbf{J} \) is defined as the current per unit area and is also a vector quantity, as it indicates the direction of current flow.

**Conclusion:** Statement 3 is correct.

### Final Conclusion
After analyzing all three statements:
- Statement 1 is correct.
- Statement 2 is misleading (the velocity of light is a vector).
- Statement 3 is correct.

Thus, the correct option is that statements 1 and 3 are correct, while statement 2 is not. Therefore, the correct answer is not "all the above" as initially suggested.