Are the points `A(3,6,9),\ B(10 , 20 , 30)a n d\ C(25 ,-41 ,5),` the vertices of a right angled triangle?

Explanation

To determine whether the points \( A(3, 6, 9) \), \( B(10, 20, 30) \), and \( C(25, -41, 5) \) are the vertices of a right-angled triangle, we can use the distance formula and the Pythagorean theorem.

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

The distance \( d \) between two points \( P(x_1, y_1, z_1) \) and \( Q(x_2, y_2, z_2) \) in three-dimensional 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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