The coordinates of the points $A$, $B$ and $C$ are given by $A\,(0,\,2,\,4)$, $B\,(4,\,6,\,11)$ and

Question

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

Accepted Answer

OD = (0,2,4) + ((3+3√3)/2)(4,1,1) or OD = (0,2,4) + ((3-3√3)/2)(4,1,1)

Finding a point to form an equilateral triangle given a line segment in 3D vectors

Finding a point to form an equilateral triangle given a line segment in 3D vectors

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