What are Vector and Scalar Quantities?

Transcript

VECTORS & SCALARS Scalars Physical quantities which can be completely specified by: 1) A number which represents the magnitude of the quantity 2) An appropriate unit are called Scalars. Scalar quantities can be added, subtracted, multiplied, and divided by usual algebraic laws. Its examples include; mass, distance, speed, density, volume, time, temperature, entropy, energy, charge, work, potential, etc.

Vectors Physical quantities which can be completely specified by 1) A number which represents the magnitude of the quantity 2) An appropriate unit 3) A specific direction are called Vectors. This means, a vector is a representation of both a quantity and a direction at the same time. Its examples include displacement, force, velocity, acceleration, and momentum.

Representation of a Vector A straight line parallel to the direction of the given vector is used to represent it. Length of the line on a certain scale specifies the magnitude of the vector. An arrow head is put at one end of the line to indicate the direction of the given vector. Unit Vector A vector whose magnitude is 1 and directed along the direction of a given vector, is called the unit vector of the given vector.

A unit vector is usually denoted by a letter with a cap over it. For example, if r is the given vector, then will be the unit vector in the direction of r such that r =.|r| or = r /|r| unit vector = vector/magnitude of the vector. Equal Vectors Two vectors having same directions, magnitude and unit are called equal vectors. Zero or Null Vector A vector having zero magnitude and whose initial and terminal points are same is called a null vector. It is usually denoted by O.

The difference of two equal vectors (same vector) is represented by a null vector. Free Vector A vector which can be displaced parallel to itself and applied at any point, is known as free vector. It can be specified by giving its magnitude and any two of the angles between the vector and the coordinate axes.

In 3-D, it is determined by the three projections on x, y, z-axes. Position Vector Position vector is the vector which represents the position of a point in a space with respect to the origin, O. It also represents the distance and direction of the points from the origin. Resolution of a Vector Splitting up a single vector into

its rectangular components is called the resolution of a vector. The rectangular components of a vector has to make an angle of 90° with each other. There’s another type of vector that you have seen but may not know about. Did you know all the graphics you are currently seeing

in this animation are also called vectors? Vector graphics is the creation of digital images through a sequence of commands or mathematical statements that place lines and shapes in a given two-dimensional or three-dimensional space. The amazing thing about this graphic is no matter how many times you zoom in to it, the quality will still be perfect and not pixelated.