A force `vecF=(2hati+hatj+hatk)N` is acting on a particle moving with constant velocity `vecv=(hati+2hatj+hatk)m//s`. Power delivered by force is

Options

A. 4 watt
B. 5 watt
C. 6 watt
D. 8 watt

Answer

To find the power delivered by the force acting on a particle moving with constant velocity, we can use the formula for power, which is given by the dot product of the force vector and the velocity vector.

### Step-by-Step Solution:

1. **Identify the Force and Velocity Vectors:**
- The force vector is given as:
\[ \vec{F} = 2 \hat{i} + \hat{j} + \hat{k} \text{ N} \]
- The velocity vector is given as:
\[ \vec{v} = \hat{i} + 2 \hat{j} + \hat{k} \text{ m/s} \]

2. **Use the Power Formula:**
- The power \( P \) delivered by the force is calculated using the dot product:
\[ P = \vec{F} \cdot \vec{v} \]

3. **Calculate the Dot Product:**
- The dot product \( \vec{F} \cdot \vec{v} \) is calculated as follows:
\[ \vec{F} \cdot \vec{v} = (2 \hat{i} + \hat{j} + \hat{k}) \cdot (\hat{i} + 2 \hat{j} + \hat{k}) \]
- Expanding this, we get:
\[ = 2(\hat{i} \cdot \hat{i}) + 2(\hat{j} \cdot \hat{j}) + 1(\hat{k} \cdot \hat{k}) + 0 + 0 + 0 \]
- Since \( \hat{i} \cdot \hat{i} = 1 \), \( \hat{j} \cdot \hat{j} = 1 \), and \( \hat{k} \cdot \hat{k} = 1 \):
\[ = 2 \cdot 1 + 1 \cdot 2 + 1 \cdot 1 = 2 + 2 + 1 = 5 \]

4. **Final Result:**
- Therefore, the power delivered by the force is:
\[ P = 5 \text{ W} \]

### Summary:
The power delivered by the force acting on the particle is \( 5 \text{ W} \).