A force `vecF=(2hati+3hatj+4hatk)N` displaces a body from position vector `vec(r_(1))=(2hati+3hatj+hatk)m` to the positive vector `vec(r_(2))=(hati+hatj+hatk)m`. Find the work done by this force.

Explanation

To find the work done by the force \( \vec{F} = (2\hat{i} + 3\hat{j} + 4\hat{k}) \, \text{N} \) when it displaces a body from position vector \( \vec{r_1} = (2\hat{i} + 3\hat{j} + \hat{k}) \, \text{m} \) to position vector \( \vec{r_2} = (\hat{i} + \hat{j} + \hat{k}) \, \text{m} \), we can follow these steps:

### Step 1: Calculate the displacement vector \( \vec{d} \)
The displacement vector \( \vec{d} \) is given by the difference between the final position vector \( \vec{r_2} \) and the initial position vector \( \vec{r_1} \):
\[ \vec{d} = \vec{r_2} - \vec{r_1} \]
Substituting the values:
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