Britannica Sources used in this answer

How are two-dimensional vectors written using coordinates?

Created from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles.

vector parallelogram for addition and subtraction — linear algebra One method of adding and subtracting vectors is to place their tails together and then supply two more sides to form a parallelogram. The vector from their tails to the opposite corner of the parallelogram is equal to the sum of the original vectors. The vector between their heads (starting from the vector being subtracted) is equal to their difference.

In linear algebra, two-dimensional vectors are typically represented using coordinates as an ordered pair of numbers, written as $(x, y)$ . These coordinates correspond to the projections of the vector onto the horizontal ( $x$ ) and vertical ( $y$ ) axes of a Cartesian coordinate system.132

Alternatively, vectors can be expressed as column vectors, which are matrices consisting of a single column with two rows:

$(\begin{matrix} x \\ y \end{matrix})$

This notation allows for the application of matrix algebra to perform operations such as addition and scalar multiplication. In this context, the coordinates represent the components of the vector, which define its magnitude and direction within the two-dimensional plane.341