Show that the points A, B and C with position vectors, ` veca=3 hat i-4 hat j-4 hat k`, ` vecb=2 hat i- hat j+ hat k`and ` vecc= hat i-3 hat j-5 hat k` respectively form the vertices of a right angled triangle.

Explanation

To show that the points A, B, and C with position vectors \(\vec{a} = 3\hat{i} - 4\hat{j} - 4\hat{k}\), \(\vec{b} = 2\hat{i} - \hat{j} + \hat{k}\), and \(\vec{c} = \hat{i} - 3\hat{j} - 5\hat{k}\) form the vertices of a right-angled triangle, we will follow these steps:

### Step 1: Find the vectors AB, BC, and AC
1. **Vector AB**:
\[ \vec{AB} = \vec{b} - \vec{a} = (2\hat{i} - \hat{j} + \hat{k}) - (3\hat{i} - 4\hat{j} - 4\hat{k}) \]
\[
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