A force `vecF=(5hati+3hatj)N` is applied over a particle which displaces it from its original position to the point `vecs=S(2hati-1hatj)m`. The work done on the particle is

Options

A. `-7J`
B. `+13J`
C. `+7J`
D. `+11J`

Answer

To find the work done on the particle by the force, 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 is given as:
\[ \vec{F} = 5 \hat{i} + 3 \hat{j} \, \text{N} \]
- The displacement vector is given as:
\[ \vec{s} = 2 \hat{i} - 1 \hat{j} \, \text{m} \]

2. **Use the Work Done Formula:**
- The work done \( W \) is calculated using the dot product of the force vector and the displacement vector:
\[ W = \vec{F} \cdot \vec{s} \]

3. **Calculate the Dot Product:**
- The dot product is calculated as follows:
\[ W = (5 \hat{i} + 3 \hat{j}) \cdot (2 \hat{i} - 1 \hat{j}) \]
- Expanding this, we get:
\[ W = (5 \cdot 2) + (3 \cdot -1) \]
- This simplifies to:
\[ W = 10 - 3 \]

4. **Final Calculation:**
- Therefore, the work done is:
\[ W = 7 \, \text{J} \]

### Conclusion:
The work done on the particle is \( 7 \, \text{J} \).