Show that the points (0,7,10), (-1,6,6) and(-4,9,6) are the vertices of an isosceles right angled triangle.

Explanation

Given points are `A(0,7,10), B(-1,6,6) and C(-4,9,6) `
We have to show that the points `(0,7,10), (-1,6,6) and(-4,9,6)` are the vertices of an isosceles right angled triangle.
so, `AB=sqrt((0+1)^2+(7-6)^2+(10-6)^2)`
`=sqrt((1)^2+(1)^2+(4)^2)`
`=sqrt(18)`
similarly `AC=sqrt((0+4)^2+(7-9)^2+(10-6)^2)`
`=sqrt((4)^2+(-2)^2+(4)^2)`
`=sqrt(16+4+16)`
`=sqrt(36)`
similarly `BC=sqrt((-1+4)^2+(6-9)^2+(6-6)^2)`
`=sqrt((3)^2+(-3)^2+(0)^2)`
`=sqrt(9+9)`
`=sqrt(18)`
As `(sqrt(18))^2+(sqrt(18))^2=(sqrt(36))^2`
which implies
`AB^2+BC^2=AC^2`
Therefore it is a right angel triangle
and we can clearly see that `AB=BC`
Hence It is a isosceles right angled triangle.