__Introduction__

__Introduction__

In vector chapter we have only one exercise and this single exercise covers a lots of subtopics. Before we discuss about the let’s know what vectors really means I mathematics.

In mathematics, a vector is a mathematical object that represents both magnitude (size) and direction. It is commonly used to describe quantities that have both a magnitude and a direction, such as displacement, velocity, and force.

A vector is typically represented by an ordered set of numbers called components or coordinates. In two-dimensional space, a vector is represented as an arrow with a certain length and a direction in the plane. The length of the arrow represents the magnitude of the vector, and the direction in which the arrow points represents the direction of the vector.

### Scalars and Vectors

The physical quantities which can be characterised by its magnitudes only is known as a *scalar quantity* or simply a *scalar*. For example: mass, density, time, speed etc.

But the physical quantity which can completely be characterised by its magnitude together with its direction is known as the *vector quantity* or simply *vector*. For example: velocity, acceleration, momentum, force etc.

### Notation and Representation

In early days, the vectors are denoted by bold faced type of letters such as a, b, AB etc.But now, we denote a vector by a letter or combination of two letters with an arrow over it. But a letter or a combination of two letters without an arrow over it means a scalar.