Vectors and their Properties
The physical quantities may be broadly classified into the vectors and the scalars. The quantities with magnitude and direction both are known as vector quantities, it means a vector is a physical quantity that has both magnitude and direction.
For Example: A car is travelling east direction along a freeway at, here we have vector called the velocity. The car is moving with magnitude of and in east direction. These two quantities, the magnitude and direction of the car, together form a vector we call velocity.
Equality of Vectors: Equality of two vectors means, they must represent the same physical quantity. Two vectors are said to be equal if their magnitudes and directions are same. Therefore, we can say that parallel translation of a vector does not bring about any change in it.
Unit Vector: Unit vector is a magnitude of 1 unit. Thus, unit vectors are used to specify the directions of vector quantities in various co-ordinates systems. In Cartesian co-ordinates, generally:
\(\widehat{i}\) = Unit Vector in x – direction,
\(\widehat{j}\) = Unit Vector in y – direction,
\(\widehat{k}\) = Unit Vector in z – direction.
Position vector of any object can be represented in Cartesian coordinates as:
\(\overrightarrow{r}\,\,=\,\,x\widehat{i}+y\widehat{j}+z\widehat{k}\).
Examples of Vector Quantities:
- Forcehas a value and a direction. You push or pull something with some strength (magnitude) in a particular direction.
- Weighthas a value and a direction. Your weight is proportional to your mass (magnitude) and is always in the direction towards the centre of the earth.