Finding a point to form an equilateral triangle given a line segment in 3D vectors
The coordinates of the points $A$, $B$ and $C$ are given by $A\,(0,\,2,\,4)$, $B\,(4,\,6,\,11)$ and $C\,(8,\,1,\,0)$.
(i)
Show that the triangle with vertices $A$, $B$ and $C$ is an isosceles right-angled triangle.
(ii)
Find the point $D$ in the same plane as $A$, $B$ and $C$ such that $BCD$ is an equilateral triangle.
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