Is there a reason why vector multiplication is the way it is. Like a intuitive reason

Is there a reason why vector multiplication is the way it is. Like a intuitive reason

>vector multiplication
No such thing.

not only is it a thing, there are multiple kinds of vector multiplications

There's a shit ton of multiplications for vectors you retard.

Dot product*

Multiply two numbers and you get another number. """Multiply""" (dot) two vectors and you get a number.

Different things retard.

thanks, that wasnt my question

If you are OP, don't feel all upity you retard, as your answer is in the fucking wikipedia page of dot product.

Take physics and you'll see why dot and cross products are defined the way they are and you'll (hopefully) get the intuition.
In short: a dot product tells you how aligned the two vectors are, and cross product tells you the area of the paralellogram contained by the two.

didnt mean to sound upity soz, i already checked wiki beforehand and couldnt figure it out
yeah, i havent yet learned physics so hopefully it does.

Well, the dot product conects an algebraic quantity to a geometric quantity. That means, that just knowing the components of vectors you can find out stuf like the angle between them. This is really nice as you can use it for a lot of stuff such as finding out if two vectors are perpendicular, or to proyect a vector on a line.

>what is dot product and vector product
Computer science majors were the absolutely most retarded when it came to this in physics classes.

EE student here. Ill try to give my own retarded explanation for this...

You have 3 common multiplication like operations on vectors (dot product, cross product and matrix multiplication)

Dot product: (scalar quantity) addresses how much of a force is in a particular direction.

Example: I want to push a box, but I'm really short compared to the box. There would be an upward component of the force I'm applying to the box. But the actual work done to the box is defined as the force ONLY in the direction of travel. Dot products will help pick the component of my force that contributes to work.

Cross product: Yeah this one is kinda tricky to me. It gives you a vector quantity, but its only defined for 3 dimensional space (as far as I know). The only way I can explain this one is that it helps define turning or torque about a point.

In physics you use it to define how fields swirl around a region of space.

Matrix Multiplication: nxm by mxh returns nxh matrix.

Matrix multiplication defines a point wise linear transformation on a set of vectors... I'm not sure of an intuitive explanation on that one.

The only times I ever use it is to take sets of equations and turn them into matrix multiplication problems, and I rarely even do that.

dot product: how much does this vector share with some other vector

cross product: see gif

>not only is it a thing, there are multiple kinds of vector multiplications
Wrong.

>Dot product*
That is not "vector multiplication".

>>what is dot product and vector product
Those are not "vector multiplication".

>Look mom I just learned basic group theory and now I'm a faggot
The term multiplication has no proper definition you fagglord.

>>Look mom I just learned basic group theory and now I'm a faggot
Who are you quoting?

>faggot
Why the homophobia?

My m8, from hs, Dillan. He was such a faggot, almost asuch as you ;)

a faggot
lrn2read

so a cross tells you the XY and the (dot) tells you where?

(You)

Are you talking about inner product (dot product)? If yes, then you're pretty much just projecting the other vector on the other vector and taking the length of that projection. There's a little more than that to it (muh negative values), but that's pretty much what it is.

(obviously you also multiply the length of the projection with the length of the vector you projected the other vector on, it gives the same result regardless of the order you choose to do it (WHY?))

You realize the picture you have there is of the cross product, not the dot product?

There is no canonical multiplication of vectors in [math] \mathbb{R}^n [\math] (I'm assuming these are the only kinds of vectors you're familiar with). There are two common products taken on this space as others have described. The intuition for the so-called dot product is much easier than the intuition for the cross product. To really understand why the cross product is defined the way it is, you should take a course of differential geometry.

Just multiply the components separately

>he just takes the dot-procuct formula as granted instead of working out how it comes out
lmaoing @ you

wut