A force `(3hati+4hatj)` newton acts on a boby and displaces it by `(2hati+3hatj)` metre. The work done by the force is

Options

A. `2`
B. `4`
C. `6`
D. `8`

Explanation

To calculate the work done by a force acting on a body that 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 \( \mathbf{F} \) is given as:
\[ \mathbf{F} = 3\hat{i} + 4\hat{j} \, \text{N} \]
- The displacement vector \( \mathbf{d} \) is given as:
\[ \mathbf{d} = 2\hat{i} + 3\hat{j} \, \text{m} \]

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

3. **Calculate the Dot Product:**
- The dot product is calculated as follows:
\[ W = (3\hat{i} + 4\hat{j}) \cdot (2\hat{i} + 3\hat{j}) \]
- Expanding this, we have:
\[ W = (3 \times 2) + (4 \times 3) \]

4. **Perform the Multiplications:**
- Calculate \( 3 \times 2 \):
\[ 3 \times 2 = 6 \]
- Calculate \( 4 \times 3 \):
\[ 4 \times 3 = 12 \]

5. **Add the Results:**
- Now, add the results of the multiplications:
\[ W = 6 + 12 = 18 \, \text{J} \]

### Final Answer:
The work done by the force is \( 18 \, \text{J} \).

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