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 solve the problem of finding the work done by the force on the body, we can follow these steps:

### Step 1: Identify the Force and Displacement Vectors
The force \( \vec{F} \) acting on the body is given as:
\[ \vec{F} = 3 \hat{i} + 4 \hat{j} \text{ Newton} \]
The displacement \( \vec{D} \) of the body is given as:
\[ \vec{D} = 3 \hat{i} + 4 \hat{j} \text{ meters} \]

### Step 2: Use the Work Done Formula
The work done \( W \) by a force when a body is displaced is given by the dot product of the force and displacement vectors:
\[ W = \vec{F} \cdot \vec{D} \]

### Step 3: Calculate the Dot Product
To calculate the dot product, we use the formula:
\[ \vec{A} \cdot \vec{B} = A_x B_x + A_y B_y \]
For our vectors:
- \( \vec{F} = 3 \hat{i} + 4 \hat{j} \) implies \( A_x = 3 \) and \( A_y = 4 \)
- \( \vec{D} = 3 \hat{i} + 4 \hat{j} \) implies \( B_x = 3 \) and \( B_y = 4 \)

Now, substituting these values into the dot product formula:
\[ W = (3)(3) + (4)(4) \]

### Step 4: Perform the Multiplication
Calculating the terms:
\[ W = 9 + 16 \]

### Step 5: Sum the Results
Adding the results gives:
\[ W = 25 \text{ Joules} \]

### Conclusion
Thus, the work done \( y \) is:
\[ y = 25 \text{ Joules} \]

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