cube of side 3 units has one vertex at one 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.
Answers
GIVEN :
Cube with one vertex (1,1,1)
Three edges from this vertex are parallel to x-axis and y and z-axes.
TO FIND :
Find the coordinates of other vertices of the cube.
SOLUTION:
◆There are many possible answers.
◆Since edges are parallel to axes, cube is placed straight in space
◆Since one vertex is (1,1,1)
Let's go to the most possible general answer of the cube being in orgin, starting from orgin, having edge length =1 cm.
◆Vertexes will be
(0,0,0)(0,0,1)(0,1,1,)(1,1,0)(1,0,0)(0,1,0)(1,0,1) (1,1,1).
◆Another example from number of possibilities is of cube starting from (1,1,1,).Here edge length should not necessarily be 1cm.
Take for 2cm,
◆(1,1,1)(1,1,3)(1,3,3)(3,3,1)(3,1,3)(1,3,1)(3,1,1)(3,3,3).
◆Draw a cube from the graph and calculate for your convenience .