VECTOR

A physical quantity having magnitude and direction and also obeying the law of vector addition is a vector quantity. A vector quantity is represented by a directed line. The length of line gives its magnitude and arrow points the direction.

All those physical quantities that need direction besides a numerical value (the numerical value often being called magnitude) along with specified units to get explained and obey the law of vector addition are known as vector quantities. Displacement, velocity (speed in particular direction), acceleration, etc are vector quantities.

The scalar quantities among themselves are added and multiplied according to simple algebraic rules, where as vector quantities are added and multiplied among themselves according to special rules.

NOTE: A physical quantity having direction may not be a vector. To be a vector, it must follow the vector law of addition and the commutative law of addition as well. e.g. Electric current is a scalar, for, it does not follow the law of vector addition. Angular displacement Δ θ (Δ θ 0) is scalar but dθ(Δ θ --> 0) is vector because dθ follow the commutative law of addition but Δ θ does not follow the same.

REPRESENTATION OF A VECTOR

To represent a vector quantity we use a straight line with arrow at one end

 ‘-->’. The length of the line is directly proportional to the magnitude of the physical quantity and arrow  gives the direction. Symbol  means vector r and simply r or  means length (magnitude) of