Show that the points `A(2 hat i- hat j+ hat k), B( hat i-3 hat j-5 hat k), C(3 hat i-4 hat j-4 hat k)`are the vertices of a right angled triangle.

Explanation

To show that the points \( A(2\hat{i} - \hat{j} + \hat{k}), B(\hat{i} - 3\hat{j} - 5\hat{k}), C(3\hat{i} - 4\hat{j} - 4\hat{k}) \) are the vertices of a right-angled triangle, we can calculate the distances between each pair of points and then check if the Pythagorean theorem holds.

### Step 1: Calculate the distance \( AB \)

The distance \( AB \) between points \( A(x_1, y_1, z_1) \) and \( B(x_2, y_2, z_2) \) is given by the formula:

\[
AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}
...