Question

The distance between the circumcentre and the ortho centre of the triangle formed by the points $(2,1,5),(3,2,3)$ and $(4,0,4)$ is

• A. $\sqrt{6}$
• B. $\frac{\sqrt{6}}{2}$
• C. $2\sqrt{6}$
• D. $0$

Answer 1

The correct option is D $0$

let the points $A(2,1,5)B(3,2,3)$ and $C(4,0,4)$
Now using distance formula in $3D$, we have
$AB=\sqrt{6}$, $BC=\sqrt{6}$ and $AC=\sqrt{6}$
Therefore, it is a equilateral triangle and as we know that the circumcentre and orthocentre in equilateral triangle coincide each other.

Therefore distance between them is $0$.