Two-Dimensional Vector Concept
In the Cartesian coordinate system, each point on a plane can be represented by a pair of numbers , where is the horizontal position and is the vertical position. The origin point is .
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In the Cartesian coordinate system, each point on a plane can be represented by a pair of numbers , where is the horizontal position and is the vertical position. The origin point is .
If we draw a straight line from the origin to another point, for example , we get a vector. This vector is often written as . A vector has both magnitude (line length) and direction (indicated by the arrow).
To simplify, we use unit vectors. Unit vectors have a length of .
Vector can be expressed as a combination of horizontal movement of and vertical movement of . In unit vector form, we write:
The values and in vector are called the vector components.
A vector with these two components is called a two-dimensional vector.
The length or magnitude of vector , written as , is the distance from the origin point to the endpoint . If is the endpoint of the vector and is the projection of point onto the -axis, we can calculate it using the Pythagorean theorem on the right-angled triangle :
Observe the following vector visualization to understand the concept of vectors in the Cartesian plane:
In this visualization, we don't use the -axis because we're working in a two-dimensional plane.
In the visualization above: