I am currently working no a linear algebra question and do not understand how to solve it. The questions gives:
Four corners of a cube are (0,0,0), (2,0,0), (0,4,0) and (0,0,10).
I am asked to find:
Find the remaining 4 corners.
Find the coordinates of the center point of the cube.
Can someone help me on the right path to this question?
How would find the other 4 corners of the cube? I dont understand how to find the width of the cube.
Thank you
On
You can tell this is not a cube because there are just three distinct distances between pairs of vertices of a given cube, and these are in the ratio $1:\sqrt 2:\sqrt 3$.
The four points you have show more than three distinct distances and the three distinct distances from the origin are clearly not in the right ratio.
The corners do not form a cube but a cuboid. They are:
$(0,0,0),(2,0,0),(2,4,0),(0,4,0),(0,0,10),(2,0,10),(2,4,10),(0,4,10)$.
The centre of the cuboid is $(1,2,5)$. These can be seen if you draw a picture.