Final answer:
The coordinate system is vital to represent vector components in two and three dimensions with Cartesian and polar coordinate systems being common. In the Cartesian system, vectors are described by their projections onto the mutually perpendicular axes, while the polar coordinate system uses radial and perpendicular vectors to define positions.
Step-by-step explanation:
The coordinate system is essential for describing vector components in graphics, whether in two-dimensional or three-dimensional spaces. Vectors in a two-dimensional plane have two components and utilize a Cartesian coordinate system with perpendicular axes marked by distances from their origin. These axes are usually labeled as x and y, with positive values to the right and above the origin and negative values to the left and below the origin. Vectors are broken down into x and y components that represent their projections onto these axes, which can be mathematically calculated using trigonometric functions when the vector's magnitude and angle are known.
In three-dimensional space, vectors have three components, adding the z-axis to the Cartesian system, which represents height above or below the plane defined by the x and y axes. Determining the components of a vector in this space involves similar methodologies but includes computation along this additional axis.
A polar coordinate system is an alternative to the Cartesian system in a plane, which uses a radial unit vector and a perpendicular unit vector to define direction and magnitude.