Q. 5 - Calculus

Question

What are the coordinates of the vertices of a cube with side length 2, whose center is at the origin, and whose faces are parallel to the coordinate planes? 

Step-by-Step Solution

Answer

Coordinates of the vertices: 

( 1, 1, 1 ); ( -1, 1, 1 ); ( 1, -1, 1 ); ( 1, 1, -1 ); ( -1, -1, 1 ); ( -1, 1, -1 ); ( 1, -1, -1 ); ( -1, -1, -1 )

Step 1. Analyzing the problem.

Since the center of the cube is at the origin, all the vertices are at 1 unit distance from the origin. But all the 8 vertices are in different coordinate planes.

Step 2. Finding coordinates.

Coordinates of the vertices: 

( 1, 1, 1 ); ( -1, 1, 1 ); ( 1, -1, 1 ); ( 1, 1, -1 ); ( -1, -1, 1 ); ( -1, 1, -1 ); ( 1, -1, -1 ); ( -1, -1, -1 )