wtf who hasnt explained dot products is the question... and its not even a good explaination... The forgot to mention many but its ok for people who dont need to understand what the dot product really is.. In fact its the worst explaination but ok for casuals..

@@AshKetchum2011 Take it easy man, many videos explain the "math" behind dot product, but she explains the highest level of understanding of what the dot product represents, this is the way how AI verifies if ideas are similar or not (yes, ideas are transformed in vectors/arrays inside Artificial Intelligence). Thanks a lot Freya @acegikmo ! Awesome and straight to the point explanation!

only one must be normalized

what i understand is that, when we want to compare the angle diferences we normalise both the vector, and if we wanted to compare the magnitude or the length or distance, then dont need to normalise it, mean one is the compare angle the other is to compare distance or range

​@@Mj-multimediaNet Depends what you want to do. Sometimes you want then not normalized. Sometimes you want only one of them normalized. And sometimes yoy want them both normalized. In this specific case you want to find cosine of an angle. So both of them should be normalized.

What does “normalize” mean? Was she showing “normalized”?

What does normalize mean

some who says simpleton is not simple

can you explain why its only right for a "unit vector" ? Just starting to understand vectors myself.

​@@MathCuriousity its because the dot product of two vectors is the length of the projected vector multiplied by the length of the vector it was projected onto, the video "Dot products and duality" by 3blue1brown explains this in a lot more detail

@@redact7395 hmm ok and why did another person say it was only ok for normed?

​@@MathCuriousity this video applies as long as the vector you are projecting onto has a length of 1 and unit vector and a normalized vector just mean that the vector has length 1

yes! but also, vectors technically don't "have an origin", they're always only the tip, in terms of the data stored

A normalized vector has a unit "length", i. e. it's a vector divided by its norm equal to itself.

@@edcify8241what would that be as an equation?

@@MathCuriousity The normalization of a vector α is α'=α/||α|| (scalar multiplication by the reciprocal of its norm), and a vector is normalized iff α'=α.

it's always the dimension of the space it's in, so in 3D it would be like a hemisphere, so you wouldn't be able to distinguish vertical from horizontal (without more math), but you would still be able to do the, "facing away" check

@@acegikmo Thank you for the clarification, Freya!

for anyone whos wondering: if you normalize one of them, you can calculate the length of the non normalized vector, because its basically checking "how often does it fit into the normalized vector (length 1) if you projected it?"

the dot product is not a vector. It is a scalar. Its just the value of "how much of one vector is contained in the other"

@@deyomash can I also say its "how much one vector opposes another" ?

@@MathCuriousity The dot product between two vectors gives a value that resembles the 'overlap' between the two. If its zero they don't "overlap" at all, which means they are perpendicular. If the dot product is simply the length of one of the two this means they are parallel. Everything else lies in between :)

yeah! the dot product is often defined using the cosine

@@acegikmo much thanks

In shaders, it can be used to tell if a normal is facing a light source or not. U can use the dot product to calculate how dark a pixel should be colored. In regular game world, a dot product can be used to tell if a player is looking at an object or not.

fresnel effect, moss on top of a stone (though it could be rotated differently if you add another vector), PBR shaders reflection of fringes (almost same thing as fresnel, really), or to generate trees and grass only on non-sloped surfaces.

also hit detection of railguns, rocket launchers, etc.

In procedural 3D modeling, I can use the dot product to determine whether part of a curve is pointing in the right direction. Or to check which parts of a polyline are near horizontal or vertical. It's more useful than calculating the angle because the dot product gives only 1 value instead of both an inner and outer angle.

it's an underdetermined problem, because we can't know the length of B or what direction B is deviating in from A (two solutions in 2D, infinite solutions in 3D) but, if you assume B has the same magnitude as A, and that the angle is signed rather than the shortest angle, it's a matter of rotating the vector A by the angle

@@acegikmo In my case, I have a Vector A which is basically Vector3.forward, (0,0,1). I have another Vector B which is used as Direction of Wind. So, for example, I want to change the direction of wind to a certain angle. I determine the angle by Vector3.Angle(VectorA,VectorB). It returns me the angle based on Value of B whatever I change. I want to turn Vector B in such a value that I get a desired Angle between the two. I suck at trignometry, so I am just not being able to visualize things, and hence cannot put it in code. I somehow managed to find some code within Unity something like this: vector2 = Quaternion.AngleAxis(targetAngle, new Vector3(0,1,0)) * Vector3.forward; I just saw this snippet and it worked. But I still am not able to comprehend it or how it works etc.

@@FaizanKhan-um6bn In 3D you need an axis to rotate around and if you want the result to be perpendicular to the original then that axis needs to be perpendicular to the original as well, so you're back to square one What you have here doesn't work in all cases, only in cases where the Y coordinate of the vector A is 0 (because in the equation the axis of rotation has Y coordinate 1). In fact it's impossibly to chose a vector that will work in all cases. One common trick that games use is to grab an arbitrary direction (eg: world up), then make a cross-product with the Vector A, then use the resulting vector (normalized ofc) as the axis of rotation ie: WorldUp = new Vector3(0,1,0); RotAxis = Vector3.Normalize(WorldUp x VecA); VecB = Quaternion.AngleAxis(targetAngle,RotAxis) * VecA; (we rotate VectorA around RotAxis by targetAngle radians) But be aware that this creates two singularities where RotAxis is undefined, when VecA and WorldUp are the same, or exact opposite. At those times the cross product will create a vector of 0 length.

@@spliter88 Hey can you explain why people are saying her video is bad because she didn't normalize? what does normalize mean? Also can you explain like I'm five your video game analogy!

@@MathCuriousity I havent seen the video in a long time so you'd have to be more specific what's their exact problem, but my guess is at some point in the video she's saying the dot product between two vectors is the cosine of the angle between them. Normalizing a vector just means turning it into a unit vector. So you just calculate its length and then divide that vector by the length. In the case of cosine, the dot product beyween two vectors is only the cosine of the angle between them if both vectors are unit vectors (ie: normalized) otherwise it'll be cosine times the length of vector A times the length of vector B

The dot product works in any number of dimensions. Just like the Pythagorean theorem.

@@edcify8241 aight, the video was about just 2D so I wasn't sure

Hi IRL sonic :D

lmaooo@@kaiandkoarivera7025

by the way, since u⋅v = v⋅u, it also works if you think : magnitude of the projection of v unto u times the magnitude of u.

yeah i was about to comment the same thing

is this because her vectors were not "normalized" whatever that means!?

@@MathCuriousity if she were to use normalized vectors, then she was right. because magnitude of v would be 1.

She is a great teacher