A force `F = (2 vec i + vec j + vec k)N` is acting on a particle moving with constant velocity ` vec v = (vec i + 2 vec j + vec k)m/s`. Power delivered by force is

Options

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

Explanation

To find the power delivered by the force acting on the particle, we can use the formula for power in terms of force and velocity:

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

where \( P \) is the power, \( \mathbf{F} \) 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 is given as:
\[ \mathbf{F} = 2 \mathbf{i} + \mathbf{j} + \mathbf{k} \, \text{N} \]
- The velocity vector is given as:
\[ \mathbf{v} = \mathbf{i} + 2 \mathbf{j} + \mathbf{k} \, \text{m/s} \]

2. **Calculate the Dot Product**:
- The dot product \( \mathbf{F} \cdot \mathbf{v} \) is calculated as follows:
\[ \mathbf{F} \cdot \mathbf{v} = (2 \mathbf{i} + \mathbf{j} + \mathbf{k}) \cdot (\mathbf{i} + 2 \mathbf{j} + \mathbf{k}) \]
- Expanding this using the properties of dot products:
\[ = (2 \cdot 1) + (1 \cdot 2) + (1 \cdot 1) \]
\[ = 2 + 2 + 1 = 5 \]

3. **Calculate the Power**:
- Since we have calculated the dot product, we can now find the power:
\[ P = \mathbf{F} \cdot \mathbf{v} = 5 \, \text{W} \]

### Final Answer:
The power delivered by the force is \( 5 \, \text{W} \).

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