How can vector quantities be represented graphically?

Answer 1

A vector is represented by a straight line of specific length having an arrow head which shows its direction. This straight line is called the representative line of that vector.

Vector variables are sometimes notated with arrow above them (particularly in handwritten physics formulae), and sometimes notated by using a bold-face font (particularly in print).

Mathematically, at least for the vectors which crop up in classical mechanics, a vector can be represented in terms of components. In 3D space, for example, we can choose a set of three independent directions (e.g. north/south, east/west and up/down) and write our vector as a sum of three parts: a purely north/south-pointing part, a purely east/west-pointing part and a purely up/down-pointing part. The length of each part gives the component of the vector in the corresponding direction (note that the north/south-pointing part counts as positive if it points north, negative if it points south, and so on).

This allows us to write such vectors in a convenient form for calculations, once a frame of reference has been agreed on. We simply list the components, writing something like

v = (a, b, c)

where v is the vector and a, b and care the components in the frame of reference being used. In this notation, basic vector arithmetic is simple. For example:

Scalar multiplication:

nv = (na, nb, nc) where n is a real number.

Vector addtion:

v1 + v2 = (a1, b1, c1) + (a2, b2, c2) = (a1 + a2, b1 + b2, c1 + c2).

Answer 2

The displacement in per unit time (i.e. in one second) and direction of travel is known as velocity. Displacement is a vector quantity as the magnitude and direction both are required to describe it like 10km east etc. So velocity is a vector quantity.

Answer 3

They can be represented by a line made with a #2 pencil. The length of the line is

made proportional to the magnitude of the vector, and some kind of identifying

mark is made on or near one end of the line to show the direction of the vector.

Answer 4

Vectors can be represented by underlining them, putting an arrow above them or by making them bold on the computer

Answer 5

The vector magnitude is described by the length and the direction in the space.

Answer 6

Scalars are represented with a real number. Vectors by a number and a direction or a location in the complex plane.

Answer 7

You can represent a vector as an arrow.