A force `( 3 hati +4 hat j)` newton acts on a body and displaces it by `(3 hat I + 4 hat j)` metere. The work done by the force is y Joules. Find y.

Explanation

To find the work done by the force on the body, 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 \( \mathbf{F} \) is given as:
\[ \mathbf{F} = 3 \hat{i} + 4 \hat{j} \text{ Newton} \]
- The displacement vector \( \mathbf{d} \) is given as:
\[ \mathbf{d} = 3 \hat{i} + 4 \hat{j} \text{ meters} \]

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

3. **Calculate the Dot Product**:
- The dot product of two vectors \( \mathbf{A} = a_1 \hat{i} + a_2 \hat{j} \) and \( \mathbf{B} = b_1 \hat{i} + b_2 \hat{j} \) is given by:
\[ \mathbf{A} \cdot \mathbf{B} = a_1 b_1 + a_2 b_2 \]
- Applying this to our vectors:
\[ W = (3)(3) + (4)(4) \]

4. **Perform the Multiplication**:
- Calculate each term:
\[ W = 9 + 16 \]

5. **Add the Results**:
- Combine the results:
\[ W = 25 \text{ Joules} \]

6. **Conclusion**:
- Therefore, the work done \( y \) is:
\[ y = 25 \text{ Joules} \]

### Final Answer:
\[ y = 25 \text{ Joules} \]