If ` hat i+ hat j+ hat k ,\ 2 hat i+5 hat j ,\ 3 hat i+2 hat j-3 hat k` and `hat i-6 hat j- hat k` respectively are the position vectors of points `A , B, C, D` then find the angle between the straight lines `A B` , `C D`. Deduce that `A B` , `C D` are collinear.

Explanation

To find the angle between the straight lines \( AB \) and \( CD \) given the position vectors of points \( A, B, C, \) and \( D \), we will follow these steps:

### Step 1: Define the Position Vectors
The position vectors are given as:
- \( \vec{A} = \hat{i} + \hat{j} + \hat{k} \)
- \( \vec{B} = 2\hat{i} + 5\hat{j} \)
- \( \vec{C} = 3\hat{i} + 2\hat{j} - 3\hat{k} \)
- \( \vec{D} = \hat{i} - 6\hat{j} - \hat{k} \)
...