Question

Verify the following:
$(0,7,-10),(1,6,-6)$ and $(4,9,-6)$ are the vertices of an isosceles triangle.

Answer 1

Let three points are $A,B,C$

Distance of :

$AB=\sqrt{(1-0{)}^2+(6-7{)}^2+(-6+10{)}^2}=3\sqrt{2}$

Similarly:

$BC=3\sqrt{2}$

and

$AC=3$

Since:

$AB=BC\ne AC$ and $AB+BC\ne AC$ not are collinier.

So it is a isosceles triangle.