Scalars are quantities that can be specified completely by a number and unit that therefore have magnitude only are called Scalars. Vectors are quantities that completely specified by magnitude and direction and that quantities follow certain rules of combination are called Vectors.
Scalars (Scalar Quantities)
Definition: "Scalars are those physical Quantities which are completely described or specified by magnitude and with suitable unit are called Scalars ".
Scalars can be manipulated by the rules of ordinary (elementary) Algebra. They are denoted by letters in ordinary type.
Scalar = Magnitude + Unit
For Example: 2 kg of Salt. (where 2 is magnitude and Kg is Unit)
Vectors (Vector Quantities)
Definition: "Vectors are those quantities that completely described or specified by magnitude, direction with suitable unit and that quantities follow certain rules of combination are called Vectors"
The word means carrier in Latin. A vector must obey the "The Law of Vector Addition".
For Example: Electric current has a direction and magnitude but do not obey vector laws of addition, hence electric current is not Vector.
Vector = Magnitude + Unit + direction
= (Magnitude + Unit) + direction
so, vector can be written as:
Vector = Scalar + direction
Representation of Vectors
A vector quantity is graphically represented by an arrow. The length of the arrow represents the magnitude of the vector say |`\vecA`| or A whereas the arrow head represents the direction of the vector say A. In text format the Boldface letters or Alphabets with arrow on the top represents the vector quantity. Mathematically it is given by:
`\vecA = |\vecA| ` `\hatA`
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