One Dimensional, Two Dimensional and Three Dimensional Vectors in Cartesian Coordinate System Physics Notes
One Dimensional, Two Dimensional and Three Dimensional Vectors in Cartesian Coordinate System:
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a pair by a pair of coordinates, which are the distances to the point from two fixed perpendicular directed lines. Each reference line is called the axis of the system, and the point where they meet is called its origin (0, 0).
Cartesian Coordinate System
1. One Dimensional Vectors: A vector that is directed along one of the axes (X-axis or Y-axis or Z-axis), is called a one-dimensional vector.
- Along X-axis, \(\vec{r}\) = xî,
- along Y-axis, \(\vec{r}\) = y ĵ, and
- along Z-axis, \(\vec{r}\)= z k̂.
One Dimensional Vectors
2. Two Dimensional Vectors: The vectors that are situated in a plane are called two-dimensional vectors. Two dimensional vectors are directed in two directions or the two axis. If the vector \(\vec{r}\) is located in X-Y plane, then the two dimensional vector \(\vec{r}\) is represented as \(\vec{r}\) = xî + yĵ, if \(\vec{r}\) is in Y-Z plane, then \(\vec{r}\) = yĵ + zk̂ and in X-Z plane, \(\vec{r}\) = xî + zk̂.
- X-Y plane, \(\vec{r}\) = xî + yĵ
- In Y-Z plane, \(\vec{r}\) =yĵ + zk̂
- In X-Z plane, \(\vec{r}\) = xî + zk̂
Two Dimensional Vectors
3. Three Dimensional Vectors: A three dimensional vector is directed in all the three axis (X-axis, Y-axis and Z-axis). If the location of point P(x, y, z) is to be represented by the vector \(\vec{r}\). Then, \(\vec{r}\) = xî + yĵ + zk̂ and hence, \(\vec{r}\) is a three-dimensional vector. Here, x, y and z are the coordinates that have the numerical values.
Three Dimensional Vectors