For example, I didn't get what is this about
#I'm not getting the purpose of dot and cross product
hot plaza
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For example, I didn't get what is this about
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hot plaza
This one is dot product
edgy briar
For example, I didn't get what is this about
One simple example of what they can be used for is to determine whether two vectors are parallel or perpendicular.
Take two vectors u and v. Then if u·v = 0, then they are perpendicular, and if u⨯v = 0(vector), then they are parallel.
Of course, there are many other applications, such as finding distances between various things (points, lines, planes), finding areas and volumes, etc.
edgy briar
but if you multiply them, won't they give you a single vector?
Cross product of two vectors does give a vector, yes.
Dot product gives a scalar.
hot plaza
What is the different between them?
I know the cross one might involve some directions since it's vector
edgy briar
Oh, you mean in a geometric sense? Hm...
Well, u⨯v is a vector that's perpendicular to both u and v, and its magnitude is equal to the area of a parallelogram constructed on u and v.
As for dot product... Well, you can think of u·v as the component of vector u along the direction of vector v, scaled by the magnitude of the latter.
swift abyss
I don't get the purpose of life we are on the same page
See dot product is the rotation of one vector with respect to another and cross product is a perpendicular vector to them both
hot plaza
Well, u⨯v is a vector that's perpendicular to both u and v, and its magnitude is...
Wait what? equal to parallelogram? that dosen't make sense since it's just a line
edgy briar
Wait what? equal to parallelogram? that dosen't make sense since it's just a lin...
Please read what I wrote more carefully.
swift abyss
U can construct a parallelogram with two given lines
edgy briar
The magnitude of cross product, not the cross product itself.
swift abyss
Consider the vector as 2 segments
Lord darpinger
I don't think your explanation is dumbed down enough for someone doing vectors first time ever
edgy briar
Hm...
swift abyss
edgy briar
Can't quite think of any simpler applications.
I mean, I can think of several applications in general, but they aren't easier than that.
swift abyss
I mean even I still don't quite know how I'd tell myself dot and cross products after solving so many sums and giving exams
hot plaza
U can construct a parallelogram with two given lines
Yes I guess only two given lines and their parallel line
swift abyss
Yes I guess only two given lines and their parallel line
Just trust that it's useful and makes sense once u do the numericals and get some understanding u can try understanding the geometrical and intuitive part
hot plaza
Alright, is there any good resource for someone who's beginner with vectors, I appreciate your help guys tho
edgy briar
I'd say just google a linear algebra textbook.
swift abyss
Alright, is there any good resource for someone who's beginner with vectors, I a...
If u were indian I'd have lot of channels for u
Youtube channels
hot plaza
If u were indian I'd have lot of channels for u
Indian 😭
hot plaza
Why not chinese
hot plaza
<:_goobertea:1290941836222791710>
Okay boss 
swift abyss
Okay boss <:_catThink:798140823941152779>
For Chinese maybe check out xiao chen cao channel
Moreover they don't have youtube
Too many problems in your question
hot plaza
Too many problems in your question
Because they consider Youtube as a distraction
jolly flax
Because they consider Youtube as a distraction
don't think so
they have other social media platforms which are just as bad
hot plaza
don't think so
Their Tiktok is way different than the one the west is using
jolly flax
it has the same brainrot content
edgy briar
I mean, I still recommend finding a textbook.
hot plaza
I have my text book that school is using, but not sure if it's that good
Would you mind if I share it to you?
edgy briar
Oh, right. Sorry, forgot we're in #1015578016606343218 .
hot plaza
No worries
edgy briar
I was thinking about this in terms of linear algebra, not geometry.
Anyway, first of all, I recommend reviewing the definition and properties of both products.
There are a lot of applications, but you need to know the properties first.
tired dagger
Dot and cross product are two different ways of “multiplying” vectors
They’re two entirely different operations however, so it’s best not to try think of them as similar things
The dot product gives you a scalar
Vaguely speaking, it gives you a scalar which measures how “similar” two vectors are
The higher the dot product, the higher the “similarity”, again, vaguely speaking
The cross product of two vectors gives you a third vector that is perpendicular to both vectors
The cross product is a very specific tool actually, since it only exists in 3D
Since only in 3D do two vectors have a unique vector which is perpendicular to both (think about it, does a cross product make sense in 2D?) Draw two non-parallel lines on a piece of paper. Can you draw a third line which is perpendicular to both lines without it sticking out the page?
The “cross product” also doesn’t exist in 4D and up since there are multiple vectors which can be perpendicular to both. (Try it yourself, say $i = (1,0,0,0), j = (0,1,0,0)$, find two vectors which are perpendicular to both $i, j$.)
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