A force `vecF=6xhati+2yhatj` displaces a body from `vecr_1=3hati+8hatj` to `vecr_2=5hati-4hatj`. Find the work done by the force.

Explanation

To find the work done by the force \(\vec{F} = 6x \hat{i} + 2y \hat{j}\) as it displaces a body from \(\vec{r_1} = 3 \hat{i} + 8 \hat{j}\) to \(\vec{r_2} = 5 \hat{i} - 4 \hat{j}\), we will follow these steps:

### Step 1: Determine the displacement vector \(\vec{d}\)
The displacement vector \(\vec{d}\) can be calculated as:
\[ \vec{d} = \vec{r_2} - \vec{r_1} = (5 \hat{i} - 4 \hat{j}) - (3 \hat{i} + 8 \hat{j}) = (5 - 3) \hat{i} + (-4 - 8) \hat{j} = 2 \hat{i} - 12 \hat{j} \]

...