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 directed line segment from the origin to another point, for example , we obtain a vector. This vector is written as . Its magnitude is the segment's length, and its direction runs from the initial point toward the arrowhead.
Two unit vectors describe the coordinate directions. Each has 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 to the endpoint . If is the endpoint and is the projection of onto the -axis, the right triangle gives its magnitude through the Pythagorean theorem:
The visualization below connects the vector, its components, and its magnitude in the Cartesian plane:
The -axis is omitted because the vector lies entirely in a two-dimensional plane.
In the visualization above:
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