Prove the the triangle with vertices a (-2,4,0), b (1,2,-1) and c (-1,1,2) is regular.

See the offered decision:

one way is to calculate (and compare) lengths of AB, AC and BC:

AB² = (-2-1) ² + (4-2) ² + (0+1) ²=14;

AC² = (-2+1) ² + (4-1) ² + (0-2) ²=14;

BC² = (-1-1) ² + (1-2) ² + (2+1) ²=14.

AB=AC=BC ⇒ the triangle is regular.