User:Silly rabbit/Vector (spatial)
From Wikipedia, the free encyclopedia
A spatial vector, or simply vector, is a geometric object which has both a magnitude and a direction. A vector is frequently represented by a line segment connecting the initial point A with the terminal point B and denoted
The magnitude is the length of the segment and the direction characterizes the displacement of B relative to A: how much one should move the point A to "carry" it to the point B.[1]
Many algebraic operations on real numbers have close analogues for vectors. Vectors can be added, subtracted, multiplied by a number, and flipped around so that the direction is reversed. These operations obey the familiar algebraic laws: commutativity, associativity, distributivity. The sum of two vectors with the same initial point can be found geometrically using the parallelogram law. Multiplication by a positive number, commonly called a scalar in this context, amounts to changing the magnitude of vector, that is, stretching or compressing it while keeping its direction; multiplication by -1 preserves the magnitude of the vector but reverses its direction.
Cartesian coordinates provide a systematic way of describing vectors and operations on them. A vector becomes a triple of real numbers, its components. Addition of vectors and multiplication of a vector by a scalar are simply done component by component, see coordinate vector.
Vectors play an important role in physics: velocity and acceleration of a moving object and forces acting on a body are all described by vectors. Many other physical quantities can be usefully thought of as vectors. One has to keep in mind, however, that the components of a physical vector depend on the coordinate system used to describe it. Other vector-like objects that describe physical quantities and transform in a similar way under changes of the coordinate system include pseudovectors and tensors.