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ELProving the famous dot product formula for the angle between two vectors.
#math #geometry #proof
@electricalmath
#Angle Between Two Vectors
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AICosine similarity measures how similar two vectors are by comparing the angle between them, making it especially useful for high-dimensional representations like embeddings (used in attention).
In transformers, this idea is closely related to how attention works: query and key vectors are compared using a dot product, which effectively captures how aligned or relevant two tokens are to each other.
When two vectors point in similar directions, their similarity is high (closer to 1), meaning one token should pay more attention to the other.
These similarity scores are then normalized and used to weight the value vectors, allowing the model to selectively focus on the most relevant parts of a sequence.
C:3blue1brown
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@aibutsimple
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AICosine similarity measures how similar two vectors are by comparing the angle between them, making it especially useful for high-dimensional representations like embeddings (used in attention).
In transformers, this idea is closely related to how attention works: query and key vectors are compared using a dot product, which effectively captures how aligned or relevant two tokens are to each other.
When two vectors point in similar directions, their similarity is high (closer to 1), meaning one token should pay more attention to the other.
These similarity scores are then normalized and used to weight the value vectors, allowing the model to selectively focus on the most relevant parts of a sequence.
C:3blue1brown
Want to Learn In-Depth Machine Learning Topics? Join 8000+ Others in our Visually Explained Deep Learning Newsletter (link in bio).
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@aitechtreding
1.9K
PHThe scalar product (also called the dot product) is a way to multiply two vectors and get a single number (scalar) as a result.
Definition
For two vectors A and B:
οΏ½
οΏ½, οΏ½ = magnitudes (lengths) of the vectors
οΏ½ = angle between them
In Component Form
If
then:
Key Properties
Commutative:
οΏ½
Distributive:
οΏ½
Zero condition (orthogonality):
If οΏ½, the vectors are perpendicular.
Geometric Meaning
Measures how much one vector points in the direction of another
If:
Positive β vectors point roughly same direction
Zero β perpendicular
Negative β opposite directions
Example
#physicsvibespk #scalarproduct #dotproduct #vector #trending
@physicsvibespk
60.0K
ALA-Level Further Maths π Further Vectors: Finding the angle between two planes π€
#Vectors #FurtherMaths #alevelfurthermaths #maths
@alevel.maths
14.0K
MA3D Vector Line Demonstration β Desmos 3D β¨π
A video demonstration showing a line passing through two points of moving vectors in 3D space, described by:
(1 - t)(xβ, yβ, zβ) + t(xβ, yβ, zβ), where -β < t < β
Created with Desmos 3D ππ₯
#3DVisualisation #VectorMaths #ParametricEquations #Desmos3D #MathsVideo #STEM #Mathematics #MathsLovers #MathsIsFun #LearnMaths #3DGeometry #LinearAlgebra #MathsVisuals #EducationalContent #GeometryLovers #MathematicsEducation #3DGraphics #DataVisualisation #StudyMaths #Algebra #Desmos #MathsCommunity #MathsExplained
@mathematics.proofs
17.1K
INCosine similarity measures how similar two vectors are by comparing the angle between them, making it especially useful for high-dimensional representations like embeddings (used in attention).
In transformers, this idea is closely related to how attention works: query and key vectors are compared using a dot product, which effectively captures how aligned or relevant two tokens are to each other.
When two vectors point in similar directions, their similarity is high (closer to 1), meaning one token should pay more attention to the other.
These similarity scores are then normalized and used to weight the value vectors, allowing the model to selectively focus on the most relevant parts of a sequence.
C:3blue1brown
Follow for more @infusewithai
#machinelearning #deeplearning #statistics #computerscience #coding #mathematics #math #physics #science
@infusewithai
1.6K
MEHow AI doesnβt understands meaning?
It understands distance and angle between two words represented as coordinates in multi dimensional vector space.
3 concepts samajh lo:
β Words = vectors
β Meaning = angles
β Similarity = cosine
@mentalhotfix
601.6K
2M#save Rotating Protractor.
Comment βPrintableβ to get yours for Free
π An acute angle measures less than 90Β° at the vertex.
π An obtuse angle is between 90Β° and 180Β°.
π A right angle precisely measures 90Β° at the vertex.
π An angle measuring exactly 180Β° is a straight angle.
π A reflex angle measures between 180Β°- 360Β°.
π A complete angle measure equals 360Β°
β
Real-life Application of Angles
π Engineers construct buildings, bridges, houses, monuments, etc., using angle measurement.
π Athletes use its concept in sports to enhance their performance.
π Carpenters use it to make equipment like doors, chairs, sofas, tables, etc.
π Artists use their measurement knowledge to sketch or create art pieces.
π Wall clocks use the concept of angles to show time with hour and minute hands.
π Angles Around Us
There are many daily life examples of an angle, such as cloth-hangers, arrowheads, scissors, partly opened doors, pyramids, edge of a table, the edge of a ruler, etc.
Continue and Follow @2monkeys.and.me for more
Like, share and save this with yoru friends
#diy #diymath #mathproblems #mathgames #mathactivities #homeschool #angles
#early #earlymathskills #earlyyearsplay #earlylearningcentre #earlychildhoodeducation #earlyyears #earlychildhood #earlyyearseducation #earlychildhoodeducator #homeschool #homeschooling #homeschoollife #homeschoolcommunity #diy #diymath #mathgamesforkids #mathgames #shapenets #kolkatablogger #kolkatamoms #kolkatamomblogger
@2monkeys.and.me
612
MARead Caption
Steps to draw an angle (using a protractor):
Draw a base line and mark a point on it as the vertex (say point O).
Place the center of the protractor on point O.
Align the baseline of the protractor with the drawn line.
Mark the required degree on the protractor scale (e.g., 60Β°, 90Β°, etc.).
Remove the protractor and draw a line from O through the marked point.
The two lines form the required angle.
#drawing #draw #angle #drawings
@maths_with_nj
1.3K
SHcbse pyq 2022 vector algebra
Q) π ππ§π π are two unit vectors such that |ππ +ππ |=|ππβππ |. Find the angle between π β ππ§π π β.
.#vectoralgebra #vectors #cbse2026
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@shivang_maths_academy_
713.4K
KRInterior Angle Sum of a Polygon
|
v
Consider an n-sided polygon
|
v
Draw diagonals from one vertex
|
v
The polygon is divided into (n - 2) triangles
|
v
Each triangle has an angle sum of 180Β°
|
v
Therefore:
Interior Angle Sum = (n - 2) Γ 180Β°
|
v
This depends only on the number of sides (n),
not the shape of the polygon.
|
v
End
@kruownmathspecialist
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