A scalar quantity is a quantity which is defined by only magnitude. Some examples of scalar quantities are Mass, Charge, Pressure, etc.
Vector quantities are those which have both magnitude and direction and obey vector laws of addition. Some examples of vectors are displacement, velocity, force, etc. A quantity is called a vector only if it follows all the above three conditions. For example, current is not a vector despite having both magnitude and direction because it does not follow vector laws of addition.
Scalars and Vectors
Following are some differences listed between scalars and vectors.
Have only magnitude
Have both magnitude and direction
Algebra: Same as real numbers
Algebra: Follow vector laws of addition
Examples: Mass, charge, etc
Examples: velocity, force, electric field. etc.
Scalar Quantities: 1. A physical quantity which is having magnitude only but not direction those are scalar quantities. 2. These are one-dimensional quantities. 3. It follows ordinary rules of algebra. 4. The scalar can be divided by any other scalar quantity. 5. It changes due to change in their magnitude only. 6. e.g. mass, work etc
Vector Quantity: 1. A vector quantity is one, that has both magnitude and direction. 2. Are multi-dimensional quantities. 3. It changes with the change in their direction or magnitude or both. 4. Follow rules of vector algebra. 5. Two vectors can never divide.
Direction of vector
Vector a shown in diagram can be represented as a=axi^+ayj^+azk^ Magnitude of vector a a = ax2+ay2+az2 ax - component of vector along x-axis ay - component of vector along y-axis az - component of vector along z- axis i^,j^andk^ - unit vectors along x,y and z direction.