A force of `2i+3j+2k N` acts on a body for 4 and produces a displacement of `3hati+4hatj+5hatk` m calculate the power?

Options

A. 5W
B. 6W
C. 7W
D. 9W

Explanation

To calculate the power exerted by a force acting on a body during a displacement, we can follow these steps:

### Step 1: Identify the Given Values
We have the following values:
- Force vector \( \mathbf{F} = 2\hat{i} + 3\hat{j} + 2\hat{k} \) N
- Displacement vector \( \mathbf{S} = 3\hat{i} + 4\hat{j} + 5\hat{k} \) m
- Time \( T = 4 \) seconds

### Step 2: Calculate Work Done
The work done \( W \) by the force on the body can be calculated using the dot product of the force vector and the displacement vector:
\[ W = \mathbf{F} \cdot \mathbf{S} \]
Calculating the dot product:
\[ W = (2\hat{i} + 3\hat{j} + 2\hat{k}) \cdot (3\hat{i} + 4\hat{j} + 5\hat{k}) \]
Using the formula for dot product:
\[ W = (2 \times 3) + (3 \times 4) + (2 \times 5) \]
Calculating each term:
\[ W = 6 + 12 + 10 = 28 \text{ Joules} \]

### Step 3: Calculate Power
Power \( P \) is defined as work done per unit time:
\[ P = \frac{W}{T} \]
Substituting the values:
\[ P = \frac{28 \text{ Joules}}{4 \text{ seconds}} = 7 \text{ Watts} \]

### Final Answer
Thus, the power exerted is \( 7 \) Watts.

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