Question

In Problems, opposite vertices of a rectangular box whose edges are parallel to the coordinate axes are given. List the coordinates of the other six vertices of the box.

$\left(0,0,0\right);\left(2,1,3\right)$

Short answer

If $\left(0,0,0\right)\&\left(2,1,3\right)$are the opposite vertex of a cuboid then other vertices are$(2,0,0),(0,1,0),(0,0,3),(0,1,3),(2,1,0),\&(2,0,3)$

Step-by-step solution

Step 1. Given Data

Opposite vertices of the cuboid are

$\left(0,0,0\right)\&\left(2,1,3\right)$

Step 2. Cuboid graph

Locate points and form a cuboid

Step 3. vertices of cuboid

vertex of cuboid on x axis is $(2,0,0)$

vertex of cuboid on y axis is $(0,1,0)$

vertex of cuboid on z axis is $(0,0,3)$

we got vertex role="math" localid="1646780142700" $(2,1,0),$on moving $1$unit from$(2,0,0)$ in y-direction

we got vertex $(0,1,3)$on moving $3$units from $(0,1,0)$in z-direction

we got vertex $(2,0,3)$on moving $2$units from $(0,0,3)$in x-direction

So all other vertices are$(2,0,0),(0,1,0),(0,0,3),(0,1,3),(2,1,0),\&(2,0,3)$