Question

A cube of side 3 units has one vertex at point (1,1,1) and the three edges from this vertex are respectively parallel to positive x - axis and negative y and z - axes. Find the coordinates of other vertices of the cube.

Answer 1

Given a cube of side 3 units has one vertex at point (1,1,1) and
the three edges from this vertex are respectively parallel to positive x - axis and negative y and z - axes.
So, x-coordinate $=1,1+3=1,4$
y-ordinate $=1,1-3=1,-2$.
z-ordinate $=1,1-3=1,-2$
The remaining coordinates are combination of above pairs:
Thus, the remaining ordinates are $=(1,1,-2),(1,-2,1),(1,-2,-2),(4,1,1),(4,1,-2),(4,-2,-2),(4,-2,1)$