Find the shortest distance between the lines `vecr = hati+hatj+lambda(2hati-hatj+hatk)` and `vecr = (2 hati+hatj-hatk) + mu (3hati-5hatj + 2hatk)`

Explanation

To find the shortest distance between the two lines given in vector form, we will follow these steps:

### Step 1: Identify the vectors and points from the line equations

The equations of the lines are given as:
1. \( \vec{r_1} = \hat{i} + \hat{j} + \lambda(2\hat{i} - \hat{j} + \hat{k}) \)
2. \( \vec{r_2} = (2\hat{i} + \hat{j} - \hat{k}) + \mu(3\hat{i} - 5\hat{j} + 2\hat{k}) \)

...