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  4. 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 -axis and z -axis. The co-ordinates of other vertices of the cube can not be:

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Q. 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 $y$ -axis and $z$ -axis. The co-ordinates of other vertices of the cube can not be:

Introduction to Three Dimensional Geometry

Solution:

image
ABCD plane is prarallel to xy plane $B (1,-2,1),\,C (4,-2,1),$
$D (4,1,1),\, E (4,1,-2),\, F (1,1,-2)$
$G (1,-2,-2),\, H (4,-2,-2)$