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How to Graph a Vector?

TopA vector can be represented by a Set of two points connected by any line. Thus vectors are directional in nature and have magnitude represented by the length of the Line Segment. The problem we are going to discuss here is how to graph a vector? Vectors can have three possible directions when they are plotted. These are given by the x, y and z planes which are also called as three-dimensional vectors. Vectors when graphed in the X and Y planes are said to be two-dimensional vectors. We have two types of Notations to describe the vectors: the matrix notation and the unit vector notation. Both can be used to describe the same vector.

To graph a vector first locate the top number of the matrix which is the value of the vector in the x-axis. Label it as "x”. Similarly, locate the bottom number of the matrix which is the value of the vector along the y-axis. Label it as "y." Now plot the Point P (x, y) onto the graph. These points can also be called as the Cartesian or Rectangular coordinates. Draw a line from the fixed point or origin O (0, 0) to the point P (x, y). This represents the direction of the vector and the length represents the magnitude of the vector as OP.
An important part to be discussed here is the Unit Vector Notation. A unit vector is the vector with unit magnitude. Represent the unit vector as x – value in front of “i” along x- axis and y – value in front of “j” along y axis. Now plot the point Q (x, y) in the graph. The same approach has to be followed for unit vector also by drawing a line from the origin point O (0, 0) to the point (x, y). The vector is now complete with its magnitude as OQ.