What are the coordinates of the vertices of a cube whose edge is 2 units one of whose vertices coincides - Maths - Introduction to Three Dimensional Geometry

Question

What are the coordinates of the vertices of a cube whose edge is 2
units one of whose vertices coincides with origin and the three
edges passing through the origin coincides with the positive
direction of the axes through the origin

Devdatta Biswas · Answer

( 0,0,0 ) ( 4,0,0 ) ( 0,4,0 ) ( 0,0,4 ) ( 4,4,0 ) ( 0,4,4 ) ( 4,0,4
) ( 4,4,4 )

One of the vertices is at the origin So, ( 0,0,0 )
Three edges coincide with the positive direction of the axes
each
With X axis ( 4,0,0 )
With Y axis ( 0,4,0 )
With Z axis ( 0,0,4 )
Three of the remaining vertices lie on planes
On XY plane ( 4,4,0 )
On YZ plane ( 0,4,4 )
On ZX plane ( 4,0,4 )
The last vertex has coordinates ( 4,4,4 )

What are the coordinates of the vertices of a cube whose edge is 2 units one of whose vertices coincides with origin and the three edges passing through the origin coincides with the positive direction of the axes through the origin