Which is a vector quantity?

Options

A. Work
B. power
C. Torque
D. Gravitational constant

Explanation

To determine which of the given options is a vector quantity, we need to analyze each option based on the definitions of vector and scalar quantities.

### Step-by-Step Solution:

1. **Understanding Vector and Scalar Quantities**:
- A vector quantity has both magnitude and direction (e.g., force, velocity).
- A scalar quantity has only magnitude and no direction (e.g., mass, temperature).

2. **Analyzing Each Option**:
- **Option 1: Work**
- Work is defined as \( W = F \cdot s \cos(\theta) \), where \( F \) is force, \( s \) is displacement, and \( \theta \) is the angle between the force and displacement vectors.
- Since work is calculated using the dot product, it is a scalar quantity.
- **Conclusion**: Work is a scalar quantity.

- **Option 2: Power**
- Power is defined as the rate at which work is done, given by \( P = \frac{W}{t} \), where \( W \) is work and \( t \) is time.
- The unit of work is joules (J), and time is in seconds (s), making power also a scalar quantity.
- **Conclusion**: Power is a scalar quantity.

- **Option 3: Torque**
- Torque is defined as \( \tau = r \times F \), where \( r \) is the position vector and \( F \) is the force vector.
- The cross product of two vectors results in another vector, which has both magnitude and direction.
- **Conclusion**: Torque is a vector quantity.

- **Option 4: Gravitational Constant (G)**
- The gravitational constant \( G \) is a proportionality constant in Newton's law of gravitation and has units of \( \text{N m}^2/\text{kg}^2 \).
- It is a constant value and does not have direction, making it a scalar quantity.
- **Conclusion**: Gravitational constant is a scalar quantity.

3. **Final Conclusion**:
- Among the options provided, the only vector quantity is **Torque** (Option 3).

### Answer:
The vector quantity among the options is **Torque** (Option 3).