A force `(3hati+2hatj)` N displaces an object through a distance `(2hati-3hatj)` m. The work done is :

Options

A. zero
B. 12 J
C. 5 J
D. 13 J

Explanation

To find the work done by a force when an object is displaced, we can use the formula for work done, which is given by the dot product of the force vector and the displacement vector.

### Step-by-step Solution:

1. **Identify the Force and Displacement Vectors:**
- The force vector \( \mathbf{F} = 3 \hat{i} + 2 \hat{j} \) N
- The displacement vector \( \mathbf{S} = 2 \hat{i} - 3 \hat{j} \) m

2. **Use the Work Done Formula:**
- The work done \( W \) is calculated using the dot product:
\[ W = \mathbf{F} \cdot \mathbf{S} \]

3. **Calculate the Dot Product:**
- The dot product is calculated as follows:
\[ \mathbf{F} \cdot \mathbf{S} = (3 \hat{i} + 2 \hat{j}) \cdot (2 \hat{i} - 3 \hat{j}) \]
- Expanding this, we have:
\[ W = (3 \cdot 2) + (2 \cdot -3) \]
- This simplifies to:
\[ W = 6 - 6 \]

4. **Final Calculation:**
- Therefore, the work done is:
\[ W = 0 \text{ J} \]

### Conclusion:
The work done by the force during the displacement is **0 Joules**.

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