Find the shortest distance between the lines `l_(1)and l_(1)` whose vector equations are
`vecr=(hati+hatj) + lambda (3hati + 4hatj - 2hatk) …(i)`
and `vecr=(2hati+3hatj) + mu (6hati + 8hatj - 4hatk) …(ii)`

Explanation

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

### Step 1: Identify the direction vectors and points on each line
The vector equations of the lines are given as:
1. \( \vec{r_1} = \hat{i} + \hat{j} + \lambda(3\hat{i} + 4\hat{j} - 2\hat{k}) \)
2. \( \vec{r_2} = 2\hat{i} + 3\hat{j} + \mu(6\hat{i} + 8\hat{j} - 4\hat{k}) \)

From these equations, we can identify:
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