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`are the position vectors of points A, B, C and D respectively, then find the angle between ` vec(AB`and `vec( C D`. Deduce that ` vec( A B`and `vec( C D`

Explanation

To solve the problem, we need to find the angle between the vectors \( \vec{AB} \) and \( \vec{CD} \) given the position vectors of points A, B, C, and D. Let's break this down step by step.

### Step 1: Identify the Position Vectors
The position vectors of the points are given as:
- \( \vec{A} = \hat{i} + \hat{j} + \hat{k} \) (which corresponds to the point \( (1, 1, 1) \))
- \( \vec{B} = 2\hat{i} + 5\hat{j} \) (which corresponds to the point \( (2, 5, 0) \))
- \( \vec{C} = 3\hat{i} + 2\hat{j} - 3\hat{k} \) (which corresponds to the point \( (3, 2, -3) \))
- \( \vec{D} = \hat{i} - 6\hat{j} - \hat{k} \) (which corresponds to the point \( (1, -6, -1) \))
...