Find the shortest distance between the lines gives by
`vecr=(8+3lamda)hati-(9+16lamda)hatj+(10+7lamda)hatk`
and `vecr=15hati+29hatj+5hatk+mu(3hati+8hatj-5hatk)`.

Explanation

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

### Step 1: Identify the lines in vector form
The lines are given in the following forms:
1. \( \vec{r_1} = (8 + 3\lambda) \hat{i} - (9 + 16\lambda) \hat{j} + (10 + 7\lambda) \hat{k} \)
2. \( \vec{r_2} = 15 \hat{i} + 29 \hat{j} + 5 \hat{k} + \mu(3 \hat{i} + 8 \hat{j} - 5 \hat{k}) \)

From this, we can extract:
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