Question

Differentiate between scalar and vector quantities. Give 2 examples of each.

Answer 1

Hint:We need to understand that all physical quantities may not be fully described by their magnitude and units alone for example if you are given the time for which a man has walked with a certain speed you can find the distance travelled by the man but you cannot find where the man has exactly reached unless you know the direction in which the man has walked therefore you can say that some physical quantities which are called scalars can be described with magnitude alone whereas the other quantities which need magnitude as well as direction are called vectors. In the above example the distance travelled by a man is scalar quantity while the final position of the man is related to his initial position i.e. his displacement can be described by magnitude and direction and hence displacement is a vector quantity

Complete step by step answer:

	Scalar	Vector
Definition:	Physical quantities which can be completely described by their magnitude alone are called scalars.	Physical quantities which need magnitude as well as direction for their complete explanation are called vectors
Specification:	They are specified by a number and a unit for example when we say that a given metal has a rod of length 5 metres it indicates that the rod is 5 times longer than a certain unit called metre does the number 5 is the magnitude and metre is the unit together they give us a complete description about length of the rod.	a vector can be represented by a directed line segment or by an arrow the length of a line segment drawn to scale give the magnitude of a vector the displacement of a body from P to Q, P Q can be represented by an arrow with the starting point p is called the tail and end point q is called the head of the arrow.
Algebra used for mathematical operations:	scalars are added or subtracted with the help of the rules of simple algebra	addition subtraction multiplication and division is done by special algebra called vector algebra
Multiplication	Scalars involve simple multiplication.	Vectors involve dot product and vector product for multiplication
Example:	Distance, speed, work, power, density are scalar quantities	Displacement, velocity, acceleration, force are examples of vector quantities

Additional information: In vector multiplication, dot product of two quantities A and B is given by
A \[ \times \]B $ = $ A B $\cos \theta $, where $\theta $ is the angle between vectors A and B .
In vector multiplication, cross product of two quantities A and B is given by
A \[ \times \]B $ = $ A B $\sin \theta $, where $\theta $ is the angle between vectors A and B .

Note:We should always remember that the dot product of two vectors gives a scalar whereas the vector product of two vectors give a vector.