Vectors & Dot Product • Math for Game Devs [Part 1] -

Vectors & Dot Product • Math for Game Devs [Part 1]

Freya Holmér
Views: 215084
Like: 7676
Welcome to my four part lecture on essential math for game developers 💖 I hope you’ll find this useful in your game dev journey!

This course will have assignments throughout, if you want to maximize your learning, I recommend doing them!

If you are enjoying this series, please consider supporting me on Patreon!

00:00:00 – Intro
00:07:05 – Why math?
00:12:59 – 1D vectors
00:36:13 – 2D vectors
01:09:35 – Vector normalization
01:15:23 – Direction to point
01:23:11 – Length
01:31:49 – Distance
01:44:14 – Point along direction
02:00:45 – Radial trigger
02:26:21 – Dot product
02:44:30 – Examples from my game
03:03:13 – Assignments
03:03:29 – Asgmt. 1 (Radial trigger)
03:05:49 – Asgmt. 2 (Look-at trigger)
03:10:03 – Asgmt. 3 (Space transformation)


Originally streamed as a course for students at , who were super kind to let me both stream this live as well as upload it here! so massive thanks to the people at FutureGames!!

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➤ Edited by Stelly:


  1. This is brilliant. Thank you Freya! Love that you're showing all these concepts in context – it's really helpful. Your students are lucky to have you 🙂

  2. I really really need to learn math for unity if i want to be successful in game development and I suck at Math.

  3. I think the understanding of a vector as a collection of numbers is a bit misleading. This way everything is based on a specific implicitly given Hamel basis.

  4. This is AMAZING! Sincerely, thank you so much for this series. I've just recently found this channel and I plan on digging through every video. You're really, really good at teaching.

  5. This is soo good. I cant even exaplain to you how useful I found this. I came with 0 knowledge of 2D/3D vector maths, it was always monkey see monkey do. But now I actually understand them. Thank you so much!!

  6. Thank you! I had a problem with understanding the whole concept of vectors, but you explained it perfectly and now I think I'm ready to use them efficiently.

  7. man, that cat is annoying. overwise, greate video (:

  8. 02:21 Funny… You got answer after 5 seconds 😀 Girl with headphones muted you instantly lol

  9. Interesting lesson.. Obvious very easy, but need paper to remember everything 😀

  10. I love that it starts with the basics,as i never had it in school.

    Is there a chance there is a good series for integrals which also starts from 0. Since I would need it for a project i had in mind for a long time(changing pitch of a voice without influencing the speed of it).

  11. The kitten is the second best part of this They have such a cute meow
    The best part is finally learning this math in a fun way after public school ruining it for me with constant homework and no purpose of learning it, being able to visualise it helps so much, thank you!

  12. I have nothing to do with dame dev but for some reason I ended up here and am absolutetely amazed by these videos. I should do so many other things, but just cant stop. Thanks a lot for this!:)

  13. Really tnx!!!!!!!!from a 35 old guy that NEVER toke more than E- in a math test(no proud of that), and now i'm going to understand FINALLY!!!(i m italian sorry for bad syntax but to lasy too for google translate hahah). Anyway REALLY TNX!!!!!

  14. 1) How about explaining the applied real wold vector application of a boat going 12 miles per hour due West on a river flowing at 7 miles per hour due East?

    2) I can use the Smith Chart, to plot the CURVES of many Impedance Vectors = {Electrical Engineering Microwaves} and calculate the Normalized Impedance and solve for the Maximum power delivered by a radar transmitter and its transmission lines' Poynting Vector for the electric field to propagate in space…. 🙂

    Great Video Learning On Vectors, Thank You.

  15. I've only randomly dipped into a her livestreams a few times and still I've learnt things just from passing by on Twitch. She's kinda awesome, making all this really good educational content available for all

  16. Hi Freya! First i want to thank you because despite i am not good in math knowledge i just saw the first part of this math course for videogames and i undersood almost all thanks to you. So im gonna to watch all the remaining parts for sure cause i think you are brilliant in the way you explain! Just one thing.. I know you probabily will not but, i would love if you could dedicate a video to understanding dots product better! I mean maybe with some pratical examples where you show few very easy calculations of dot products and how to apply it! I tryed watching videos from other people for this part but they are not so explicit to understand as you are good to do! Thanks a lot again!

  17. The introduction of numbers as coordinates is an act of violence.

  18. such a useful i know alot and i will finish all soon really big thanks 😀

  19. On throughout whole lesson a cat meow behind ^_^

  20. Hi Freya do you remember me that annoying guy from the beziér curves video? I understand now that video is more an overall look about that theme so it's fine the way you've donne it. I've watched some parts of this long video and the way you explain the math the logic is almost perfect if not perfect. But i think u should and use "real life examples" instead of using points and lines to demonstrate things and it seems you only do that when someone asks you, use missiles going towards a player, asteroids breaking n following a player etc… That's why there's always someone that has the courage to ask u to show an example cuz they really wanna associate to a real need what you've explained. Rember what i've said "code it in the most simple way". You have some lines like .normalize, .distance etc… I don' t know if that comes from a different video the code you have inside but even so u should always right the code from scratch.
    You explain so well the math, the logic all of this on that "kinda of photoshop presentation" that becomes so easy to understand that the hard(althoug easy too) part is really getting the hands on the code. It's not theory that will make us understand but practice and practice in the right way. If i had your knolwedge i would spend much less time with presentations and create real scenarios. But anyways thanks for your work.

  21. Very epic stuff, thank you.

  22. I personally like to think about negation as a 180° rotation instead of a « flip » because once you learn about Complex numbers it will make so much more sense. A rotation is a vector multiplied by a complex number. Rotate twice, multiply by the square of that complex number. So 180° is the same as rotating by 90° twice. so to rotate by 90° you multiply by the square root of -1 = i

  23. Sure I've used algebra! I cosine'd on a house once. Only once. Also, what social skills?! #py-thag-or-ean

  24. I've decided I'm not going to go to University anymore since the professors don't teach you anything except tell you what you need to learn. I think everyone is capable enough to do a simple google search and learn new things. You're awesome and thank you for being my math professor.

  25. What I don't understand at 2:33:19 regarding the dot product is. If B is longer than A won't the scalar projection of B to A (extending to infinity) always be greater than 1?

  26. Amazing contents and I LIVE for the cat screaming in the background while the lecture was ongoing🐱
    Thank you for doing this🙏

  27. Could You please share the series of Math for 3D Game, like 3D Euler Rotation, Quaternion etc?

  28. Hello Freya how could i use is radial trigger use collider

  29. Thank you Freya I learn a lot plus your game is beautiful I like it

  30. These series are something I've been searching for for a long time. I set a goal to watch every math tutorial and work hard. Thank you for making these videos for strangers like me who need them

  31. Freya I didn't get how to we can move the direction vector by just adding it with the vector you want to move to??

  32. Your cat needs to get married … Which makes my cat over here gets crazy when she hears that sound.

  33. I can understand the logic but am having hard time with code ,what should i do pls??

  34. That RGB = XYZ stuff was very clever and cool

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