Vectors: What's to know about them?

in StemSocial10 months ago (edited)

Air traffic controllers, physicists, and video game creators do not have a lot in common, except for the basic concept of "Vectors." You've undoubtedly heard this term thrown about a lot but perhaps you're just like me and you just aren't really sure what it means. That's fine; this post will likely answer a few of our questions. What exactly are vectors? And why should they be important to anyone?

vector_from_a_to_b.svg.png
{vec {a}} is a vector from point A to B. ; Author ; License

First and foremost, we must grasp the concept of "scalars," which means "quantity with magnitude." Scalars are units of measurement that tell us how much of anything there is. The distance between you and your television, for example, is scalar, as is the volume and temperature of the coffee you most likely drink in the mornings.

The magnitude of vector quantities is also accompanied by an additional piece of information known as "direction." You'll need to know how far away and in which direction your kitchen is in order to go there and create some pancakes. This time, it's not just the distance that matters, but also the displacement.

Because vectors do not change depending on perspective and remain invariant to the coordinated system, they are highly unique and valuable in a variety of domains. You might be wondering what that means.

This question can be answered by taking a cue from this: if you and your friend are standing on opposite sides of a box you want to move. This means you're facing opposite directions. If your friend takes two steps to the right and three steps forward while you take two steps to the left and three steps back, you'll likely feel like you're moving in different directions, but in reality, you've both moved the same distance in the same direction by following the same vector. The vector remains constant and unchanged regardless of which way you face or which coordinate system you set over the ground.

Taking a look at the x and y axes of the well-known cartesian coordinate system. Because both directions are utilized to define everything we graph, they are referred to as the coordinate basis. Moving the box from point A to point B produces a vector from point A to point B, which can be expressed mathematically as 2x + 3y or as an array (2,3). Your coordinate basis points in the opposite directions as your friend's and can be written as -2x'-3y' or as an array if you're looking the other way (-2,-3).

graph_vec.png
[Source:@mengene)

The arrays are clearly not the same, yet a vector cannot be described entirely by an array. Each array requires a basis to provide context, and when they are appropriately assigned, it is clear that they are describing the same vector. Individual elements in the array can be thought of as letters, and just as a sequence of letters can only make up words in a specific language, when given a coordinate basis, an array takes on the meaning of a vector. Similarly, distinct representations from two bases can describe the same vector, just as different words in two languages can express the same meaning. The vector is the essence of what is being communicated, regardless of the language used to describe it.

Because all quantities with this attribute are members of a group called Tensors, scalars likewise have this coordinate invariance property. Varying forms of tensors hold different quantities of data. One might wonder if this suggests that something other than vectors can transmit more information. Yes, most definitely!

Even if you have forces working in the same direction with equal amplitude depending on how they are oriented, you might witness waves or whirls if you were to develop a video game and you'd like to genuinely simulate how water behaves. Orientation is achieved by combining force (which is a vector) with another vector. The physical quantity "stress," which is an example of a second-order tensor, is a physical quantity.


A clip of how Tensorflow is applied in Building A Video Game

Outside of video games, tensors are utilized for a variety of applications, including scientific simulations, car design, and brain imaging. Scalars, vectors, and the tensor family provide a very simple means of understanding complicated ideas and relationships, and they are a prime example of mathematics' elegance, beauty, and essential usefulness.

Thanks for reading through!

More interesting reads can be found here:
An introduction to vectors
Vectors
Scalars and Vectors
Applications of Vectors in Real Life, Engineering and Physics.

Posted from HypeTurf

Sort:  

Thanks for this very clear post, to which I have not much to say. As a side note, I am always surprised how the notion of vectors is not fully mastered by all students after a first year of bachelor in science in my university... I know it is also the case in some other universities from different countries...

By the way, the first image does not display correctly on condenser (hive.blog).

The case is the same in m country! Perhaps more emphasis needs to be put on ensuring students understand and master the concept of vectors for it is quite elementary yet important!

And i have reuploaded the image to display correctly on condenser.. Thank you!

The real issue is that the university system is such that you can pass to the following year while failing some courses. As long as the average mark is above 10, you are good to go.

With such a system, students with gaps in their knowledge background can pass from one year to the next one, and gaps accumulate... There is unfortunately not much we can do here as the majority is strongly against changing anything to the current configuration (I do not belong to this majority, FYI).

I find this quite interesting :) I'll admit I'm a product of this system and that is why I have tried to learn a lot of new things on by myself. An alternative system would be nice, but i bet the other system would probably have it's own lapses as well.

There is no perfect system, and a constant of motion is that "it was better before". Regardless of the period we live, this sentence has always been raised...

At the end, I agree that having alternative is what is important. In our university, we now develop parallel formations in which you must succeed all courses to pass to the next year, and have an average mark of 12/20 instead of 10 to pass. If those conditions are not met, there is still a possibility to pass to the next year, this time according to standard rules. However, the student is re-injected in the main formation and not into the new one that is more restrictive. Obviously, the diploma eventually obtained are slightly different.

Sounds efficient. The student comes out a better product with such a strategy. Education will continue to evolve and i hope it gets better! There is so much knowledge out there and it's getting easier to source for it by the day!

i should come enrol in your school.. hhahhaa :)

I definitely agree with what you wrote here.

i should come enrol in your school.. hhahhaa :)

You can apply. Enrollment season is open at the moment. I however cannot guarantee anything as any external candidate's application is reviewed by an ad-hoc committee.

I'll sure try to check it out! Thanks

@tipu curate 2

Thanks for your contribution to the STEMsocial community. Feel free to join us on discord to get to know the rest of us!

Please consider delegating to the @stemsocial account (85% of the curation rewards are returned).

You may also include @stemsocial as a beneficiary of the rewards of this post to get a stronger support.