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 calculate the lengths of the sides of the triangle formed by these points and then check if the Pythagorean theorem holds.

### Step 1: Calculate the length of side AB
The length of side AB can be calculated using the distance formula:
\[ AB = |\vec{B} - \vec{A}| \]
Calculating \(\vec{B} - \vec{A}\):
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