Question
Define vector
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GPT 3.5
In mathematics and physics, a vector is a mathematical entity that represents both the magnitude (size) and the direction of a quantity. It is often represented as an arrow with a specific length and direction in a coordinate system.
A vector can be described by its components, which are numerical values that indicate the magnitude of each coordinate in a specific coordinate system. For example, in a 2-dimensional coordinate system, a vector can be written as (a, b), where 'a' represents the magnitude along the x-axis and 'b' represents the magnitude along the y-axis.
Vectors can be added together or multiplied by a scalar to produce new vectors. The addition of vectors follows the parallelogram rule, where the vectors are placed head to tail and the resultant vector is drawn from the tail of the first vector to the head of the second vector.
Vectors have various applications in mathematics, physics, and engineering, such as representing forces, velocities, displacements, electric fields, and more.
A vector can be described by its components, which are numerical values that indicate the magnitude of each coordinate in a specific coordinate system. For example, in a 2-dimensional coordinate system, a vector can be written as (a, b), where 'a' represents the magnitude along the x-axis and 'b' represents the magnitude along the y-axis.
Vectors can be added together or multiplied by a scalar to produce new vectors. The addition of vectors follows the parallelogram rule, where the vectors are placed head to tail and the resultant vector is drawn from the tail of the first vector to the head of the second vector.
Vectors have various applications in mathematics, physics, and engineering, such as representing forces, velocities, displacements, electric fields, and more.