Find shortest distance between the line
`vecr = (5hati + 7hatj + 3hatk )+lambda (5hati-6hatj+2hatk)and vecr = (9hati+13hatj+15hatk)+s (-3hati+hatj-hatk)`

Explanation

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

### Step 1: Identify the lines and their direction vectors
The vector equations of the lines are given as:
1. Line 1: \(\vec{r_1} = (5\hat{i} + 7\hat{j} + 3\hat{k}) + \lambda(5\hat{i} - 6\hat{j} + 2\hat{k})\)
2. Line 2: \(\vec{r_2} = (9\hat{i} + 13\hat{j} + 15\hat{k}) + s(-3\hat{i} + \hat{j} - \hat{k})\)

From these equations, we can extract:
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