"Find a point R in the 3-dimensional space such that the points (0, 0, 0), (1, 2, 3), (2, 2, ?2), and R form a rectangle"
Could somebody please give me some direction as to how I would go about answering this question? Help is greatly appreciated, thanks!
The 4th point would be the sum of the vectors {1,2,3} + {2,2,-1} = {3,4,1}.
And of course David already gave you the solution:
Then the displacement to the point R would be the sum of the displacements to the second and third point. So what is it?
Jordan, a quick and dirty solution, using a CAD program, gives the point {3, 4, 1}. This is how it looks in Mathematica:
Graphics3D[ Polygon[{{0, 0, 0}, {1, 2, 3}, {3, 4, 1}, {2, 2, -2}}], Axes -> True, AxesOrigin -> {0, 0, 0}, Boxed -> False ]
Hi David, thank you for your response. Could you provide me with your answer to see whether I have arrived at the same conclusion?
The three vectors (better expressed as Mathematica Lists with curly brackets) are the displacements of the three points from the origin. To define a plane the three of them should not be scalar multiples of one another. {0,0,0} is a scalar multiple of the other two but Is the third point displacement a multiple of the second point displacement?
{0,0,0}
In fact, to be part of a rectangle, the second and third displacements must be at right angles, which means their dot product is zero. Is it?
