Vector Calculus
VECTOR
Vector - Definition
Any physical quantity that has to be defined by both magnitude and direction is called as vector.
Vector = magnitude & direction
Magnitude:
Magnitude is just a number (with unit of the quantity) that quantifies the physical quantity.
For example, $10^{\circ}C$, $5\;N$, etc.,
Direction:
Direction shows how a vector is directed in a two or three dimensional space.
Unit Vector:
As we know, vector is nothing but a combination of magnitude and direction. $$Vector=Magnitude\;Direction$$What happens if we divide the vector with its magnitude?. $$\frac{Vector}{Magnitude}=Direction$$Which is nothing but the direction of the vector. Right???
Also, We can say, that vector’s magnitude gets nullified (i.e) becomes unity. Hence we can call it as unit vector.
By comparing the above two statements, we can say, unit vector is nothing but a vector with unit magnitude used solely to represent the direction of the vector.
Unit vector is nothing but a vector with unit magnitude used solely to represent the direction of the vector.
Now,
Vector = Magnitude & Unit vector