Physics

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.

S.No. | Scalars | Vectors |

1. | Have only magnitude | Have both magnitude and direction |

2. | Algebra: Same as real numbers | Algebra: Follow vector laws of addition |

3. | Examples: Mass, charge, etc | Examples: velocity, force, electric field. etc. |

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

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.

$a=a_{x}i^+a_{y}j^ +a_{z}k^$

Magnitude of vector a

a = $a_{x}+a_{y}+a_{z} $

$a_{x}$ - component of vector along x-axis

$a_{y}$ - component of vector along y-axis

$a_{z}$ - component of vector along z- axis

$i^,j^ andk^$ - unit vectors along x,y and z direction.