### Bring Me Vector - Basics

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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.

And to find out the magnitude of a vector that is not in the standard position, we can simply use the formula used to calculate the distance between two points.
As discussed in the previous article What`s The Point? Adding a 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.

In a 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.
And similarly, in a three-dimensional space, the dimensionality of the below vector is 3.

### What`s the Point?

Here`s the point : "A point is a fundamental notion , which describes an absolute position in a defined   space . It does not have any particular intrinsic meaning but is used as a reference within the context of a defined space . A point can be seen as a zero-dimensional entity". Breaking down the above statements to understand the idea of a point in a defined space, we need to understand what is a defined space. A defined space consists of various points and the  arrangement between the points. And that defined space can be anything. We can consider the universe as the defined space, spanning in all directions indefinitely. Imagine a string of beads. Here, if we consider that each bead does not have any intrinsic property like shape, length, width... etc, i.e each bead is a point. As they are arranged in an order, each bead describes the absolute position(i.e order) of that particular bead in the context of the above-defined space. You can learn more about vario

### Midnight Musings - One True Desire

I still have a lot of questions. But it all boils down to just this. I`m a conscious being and what would be the one thing I truly desire. That's all that matters. Someone may ask me, Why only one desire? Because I am driven by desire. And it's hard to quench my thirst for any desire absolutely. I pretend to be satisfied. But in the deepest corners of my heart, when I try to find the answer, I don't know if I am!. I may be convincing myself and others around me that I am!. So then comes the question, Can I be ever truly satisfied with what I have?. And why there is a need to be? That's an interesting question!. To understand, Let me get into discussing more ideas of desire in my words. Desire can be compared to being in quicksand. When you give in to the quicksand, you will slowly engulf yourself in it. This is what is happening within me, I hold no control over my desires, but when I don't fight them, I slowly sink in. But, let us say, I want to get out of it. The

### First post - A short dream

I just wished to be that which I was not. And just by that mere intention,  I was put on the other side of the door and it got locked!. In confusion, I started crying... I was able to sense something new.  And going forward I was told that I was born. And  gradually I forgot what I was before this. In this illusion I fell,  I wandered , I laughed, I cried ... And  every time I felt the extremities of the illusion I  understood that something was missing. I was not sure what it was,  maybe in my life, maybe in myself. But there was something that was calling for me all along.  This went on for a long time... I indulged myself in various things, none of them being anything out of the ordinary. But suddenly one day miraculously I find a key  and I started to remember the door.  Even b efore I could open the door with the key,  she opened the door!... She asked me "Are you done playing, my child ?".  Then there was a realization "Mother never left! I was just dreaming and s