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
The displacement vector \(\vec{d}\) can be calculated using the formula:
\[ \vec{d} = \vec{r_2} - \vec{r_1} \]
Substituting the given vectors:
...