In this article, I`m going to explain the very basics of vectors. Then in the upcoming articles, I`m going to explain more concepts like span, subspace, basis vectors, vector components... etc.

"A **vector** is a **geometrical** **object with** both **magnitude** and **direction**. In simple words, it's a **directed** **line** **segment**, from two points **A** to **B**, where the **line segment's length is the vector's magnitude and the line's direction** from A to B is the **direction** of the vector AB. "

Well, that's quite a mouthful. I would advise the readers through my previous blog article What`s The Point? to understand more about the concepts of point and line.

Now, let us try to understand the above-provided definition of a **vector** by understanding line segments. A **line segment** is a **line** between two **points**. And a **line **is nothing but an infinite set of points. So ultimately a line segment is an infinite set of points between two points.

Now imagine a **two-dimensional **space where we have identical line segments scattered all over the space.

Identical How? you may ask me. Because all of those line segments **rise** **1-**unit with respect to the **y-axis** and **run** **1-**unit with respect to the **x-axis**. Every line segment has a **starting point** and an **ending point**. Let us call the **starting point** as **tail **and the **ending point** as **head**. Now if you observe, in the above two-dimensional space, every line segment`s tail and head are different. i.e. the cartesian points of the head and tail are different for all the line segments. But the idea that we are more interested in here is the **direction** of the line segment. All the line segments in the above two-dimensional space are pointing in the **same direction**. In that sense that they are pointing in the same direction and have the same rise and run with respect to the two-dimensional space we can call these line segments identical.

To understand the idea of **head** and **tail**, you can go through the below diagram.

But an important thing to know is that the head **B(1,1) **is not equivalent to the cartesian point **(1,1)**. Because the line segments tail is not starting from the origin i.e **(0,0)**.

When a line segment`s tail is the origin **(0,0)**, then that line segment or **vector** is said to be in the **standard position**. Also, **AB** is said to be the **positional vector of point B** when point A is the origin.

So a **vector** that is in standard position can be simply represented by its **head**, as below.

A vector can be represented in two ways, a **row vector**, or a **column vector**.

**magnitude**of the vector is nothing but the length of the line segment. And it can be calculated by using the

**Pythagoras**theorem.

**dimension**means adding a

**degree of freedom**to the

**point**. Imagine the vector is present in the standard position, the

**dimensionality of a vector**is the

**number of elements**in the vector.

**one-dimensional**space (number line), the

**dimensionality**of the vector below is

**1**, And in a

**two-dimensional**space, the

**dimensionality**of the vector below is

**2**.

**three-dimensional**space, the

**dimensionality**of the below vector is

**3**.

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