Q. 273.8( 11 Votes )

A vector has both

Answer :

A vector quantity is one which has both magnitude and direction but should also obey laws of vector addition subtraction and multiplication for e.g. Electric Current has both magnitude and direction but is not a vector it is added algebraically not vectorially so it is a scalar quantity suppose current I1 and I2 are flowing as shown in figure both have same magnitude the net current is I = I1 + I2 = 2 I1 = 2I2


If if we would have added them using vector laws, both are equal in magnitude and opposite in direction so resultant would have been zero which is incorrect so current is not vector



likewise, all quantities having both magnitude and direction are not vectors


Now suppose a body is rotating about a fixed axis and has rotated by an angle 𝜽 now we have both direction of axis of rotation and the angle of rotation, but this rotation is not a vector because direction of rotation cannot be specified with these two quantities suppose there is a particle at A reached B


as shown in figure



Now direction of rotation is continuously changing and the total angle of rotation 𝜽 describe the magnitude of rotation but the direction cannot be specified but if we take an very small angle of rotation i.e. at each instant direction can be specified when we are considering change in angle is very small i.e. instantaneous change in angle of an rotating body d𝜽 and they obey the law of vector algebra as well and direction can be specified as tangential direction as shown in figure



So we can see if we take very small instantaneous angle of rotation then rotation is vector but if we take large angle direction cannot be specified and hence it’s not a vector so every rotation is not vector i.e. any rotation is not vector


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