Question

A cube of side 5 has one vertex at the point (1,0,-1), and the three edges from this vertex are, respectively, parallel to the negative x and y axes and positive z-axis. Find the coordinates of the other vertices of the cube.

• A. (1,0,1),
• B. (0,-1,0),
• C. (0,0,-1),
• D. (1,0,0)

Answer 1

The correct option is B (0,-1,0),

Consider the problem

Below, are four complete cube face on $XZ-plane,(y=0)$

Given point

$(1,0,-1)$

End of the edge parallel to negative $x-axis$

$(0,0-1)$

Origin

$(0,0,0)$

End of the edge parallel to positive $z-axis$

$(1,0,0)$

And, below

Four point complete the opposite face of cube.

consider $P$, end of edge parallel to negative $y-axis$

$(1,-1,-1)$

Edge from $P$ parallel to positive $z-axis$

$(0,-1,0)$

Edge from $P$ parallel to negative $x-axis$

$(0,-1,-1)$

And

$(0,-1,0)$