Find the shortest distance between the lines `vecr=(hati+2hatj+hatk)+lamda(2hati+hatj+2hatk) and vecr=2hati-hatj-hatk+mu(2hati+hatj+2hatk)`.

Explanation

To find the shortest distance between the two given lines, we can follow these steps:

### Step 1: Identify the lines and their components
The given lines are:
1. \(\vec{r} = \hat{i} + 2\hat{j} + \hat{k} + \lambda(2\hat{i} + \hat{j} + 2\hat{k})\)
2. \(\vec{r} = 2\hat{i} - \hat{j} - \hat{k} + \mu(2\hat{i} + \hat{j} + 2\hat{k})\)

From these equations, we can extract the following:
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