Verify the following: (0,7,10), (-1,6,6) and (-4,9,6) are vertices of a right angled triangle

Explanation

To verify that the points \( A(0, 7, 10) \), \( B(-1, 6, 6) \), and \( C(-4, 9, 6) \) are the vertices of a right-angled triangle, we will use the distance formula and the Pythagorean theorem.

### Step 1: Calculate the distances between the points

The distance \( d \) between two points \( (x_1, y_1, z_1) \) and \( (x_2, y_2, z_2) \) in 3D space is given by the formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} \]
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