Final answer:
Two lines in the same plane are coplanar, a fact used extensively in geometry and vector analysis. The Cartesian and polar coordinate systems are useful for resolving vectors in a plane, with coplanar lines being fundamental in these calculations.
Step-by-step explanation:
If we consider two lines within a given plane, we can indeed say that they are coplanar. By definition, when two or more lines reside on the same flat surface or plane, they are referred to as coplanar. This concept is fundamental in geometry and is quite essential when resolving vector problems or addressing issues in three-dimensional space.
In terms of vectors on a plane, if we were to have a two-dimensional vector problem in which no two vectors are parallel, one efficient method of solving the problem would be to choose a coordinate system with one horizontal axis (x) and one vertical axis (y), known as the Cartesian coordinate system. This system allows us to work with vectors using unit vectors i and j along the x-axis and y-axis respectively. On the other hand, another common coordinate system used for resolving vectors in a plane is the polar coordinate system, which uses a radial unit vector F indicating the direction from the origin and a unit vector t that is orthogonal to the radial direction.
The solution to vector problems often involves projecting vectors onto these axes, either using the parallelogram rule to find a resultant vector for two vectors, or the tail-to-head method for multiple vectors. Understanding the concept of coplanar lines and using these principles of vector addition are vital in analyzing forces that act perpendicular and parallel to surfaces, as in physics applications, for instance.