Which coordinate system categorizes positions using three perpendicular axes?

Which coordinate system categorizes positions using three perpendicular axes?

• A. Cartesian Coordinate System
• B. Cylindrical Coordinate System
• C. Spherical Coordinate System
• D. Polar Coordinate System

Answer: (A)

The main idea here is that three mutually perpendicular directions define a Cartesian coordinate system. In this system you locate a point by measuring along x, along y which is perpendicular to x, and along z which is perpendicular to both. This orthogonality makes coordinates straightforward to work with in 3D, and distances between points follow the Pythagorean relation. Other coordinate systems describe points with r and angles in a plane (polar), or combine a radial distance, an angle, and height (cylindrical), or a radial distance with two angles (spherical). Their coordinate lines aren’t defined by three fixed perpendicular axes in space, so they don’t match the description of three perpendicular axes as cleanly as the Cartesian system does.

The main idea here is that three mutually perpendicular directions define a Cartesian coordinate system. In this system you locate a point by measuring along x, along y which is perpendicular to x, and along z which is perpendicular to both. This orthogonality makes coordinates straightforward to work with in 3D, and distances between points follow the Pythagorean relation.

Other coordinate systems describe points with r and angles in a plane (polar), or combine a radial distance, an angle, and height (cylindrical), or a radial distance with two angles (spherical). Their coordinate lines aren’t defined by three fixed perpendicular axes in space, so they don’t match the description of three perpendicular axes as cleanly as the Cartesian system does.