A force `(4hati+hatj-2hatk)` N acting on a body maintains its velocity at `(2hati+2hatj+3hatk) m s^(-1)`. The power exerted is

Options

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

Explanation

To solve the problem, we need to calculate the power exerted by the force acting on the body. The power can be calculated using the formula:

\[ \text{Power} (P) = \mathbf{F} \cdot \mathbf{V} \]

where \( \mathbf{F} \) is the force vector and \( \mathbf{V} \) is the velocity vector.

### Step-by-step Solution:

1. **Identify the Force and Velocity Vectors:**
- The force vector \( \mathbf{F} = 4\hat{i} + \hat{j} - 2\hat{k} \) N
- The velocity vector \( \mathbf{V} = 2\hat{i} + 2\hat{j} + 3\hat{k} \) m/s

2. **Calculate the Dot Product \( \mathbf{F} \cdot \mathbf{V} \):**
- The dot product is calculated as follows:
\[ \mathbf{F} \cdot \mathbf{V} = (4\hat{i} + \hat{j} - 2\hat{k}) \cdot (2\hat{i} + 2\hat{j} + 3\hat{k}) \]
- This expands to:
\[ = 4 \cdot 2 + 1 \cdot 2 + (-2) \cdot 3 \]

3. **Compute Each Term:**
- Calculate \( 4 \cdot 2 = 8 \)
- Calculate \( 1 \cdot 2 = 2 \)
- Calculate \( -2 \cdot 3 = -6 \)

4. **Sum the Results:**
- Now, sum the results of the dot product:
\[ 8 + 2 - 6 = 4 \]

5. **Conclusion:**
- Therefore, the power exerted by the force is:
\[ P = 4 \text{ watts} \]

### Final Answer:
The power exerted is **4 watts**.