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:

\[ P = \vec{F} \cdot \vec{v} \]

where \( P \) is the power, \( \vec{F} \) is the force vector, and \( \vec{v} \) is 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. **Calculate the Dot Product:**
- The dot product \( \vec{F} \cdot \vec{v} \) is calculated as follows:
\[ \vec{F} \cdot \vec{v} = (2\hat{i} + \hat{j} + \hat{k}) \cdot (\hat{i} + 2\hat{j} + \hat{k}) \]
- Using the properties of dot product:
\[ = 2 \cdot 1 + 1 \cdot 2 + 1 \cdot 1 \]
- Simplifying this gives:
\[ = 2 + 2 + 1 = 5 \]

3. **Determine the Power:**
- Thus, the power delivered by the force is:
\[ P = 5 \text{ Watts} \]

### Final Answer:
The power delivered by the force is **5 Watts**.

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