Types of vector

Types of vector

Aug 08, 2022, 16:45 IST

Vectors and Scalars, addition of vectors, components of a vector in two dimensions and three dimensional  space, scalar and vector products, scalar and vector triple product, Application of vectors to plane geometry.

About Vector

A vector may be described as a quantity having both magnitude and direction.

Geometrically a vector is represented by a directed line segment as shown in the adjacent figure. The direction is indicated by the length of the segment AB. A is called the initial point and B the terminal point of

A scalar is quantity, having magnitude only. In other words, a scalar is just a real number.

Displacement, velocity, momentum, area are some examples of vectors while distance, speed, volume temperature are just scalars.

FREE VECTORS

Vectors which are fully characterized by the magnitude and direction only are called free vectors and those are fully characterized by the magnitude, direction and also line of support are called line (or bound) vectors.

Displacement, velocity are free vectors while force and moment of a force about a point are line vectors.

Free Vector: A free vector is not located in any particular position.

POSITION VECTOR OF A POINT

We take arbitrarily any point O in space to be called the origin of reference.

ANGLE BETWEEN TWO VECTORS

It is defined as the smaller angle formed when the initial points or the terminal points of two vectors are brought together.

MULTIPLICATION OF A VECTOR BY A SCALAR

Given a vector and a scalar kR, then k  (or  k) denotes a vector whose magnitude is   i.e., k times that of  and whose direction is the same or opposite to that of  according as k > 0 or k < 0 respectively. Also, 0  =  , zero or null vector which has zero magnitude and arbitrary direction.