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How to Find the Angle Between Two Planes Given by Their Equations | MOA Lesson 25
Hey math fans!
Welcome to Math Olympiad Academy,
Lesson 25 is now live on MOA:
By the end of this video, students will be able to:
Identify the normal vector for each plane from its equation
Use the dot product to compute angles between plane
Determine when planes are perpendicular or form acute angles
Apply vector reasoning systematically in 3D geometry
Approach advanced spatial problems with confidence and structure
Watch the complete step-by-step lesson for free on YouTube by searching โMOA Lesson 25โ.
or access it directly via the link below:
We sincerely thank our subscribers and all viewers for your continued support.
The MOA Team
AI๋ ์ซ์๋ก ์ธ์์ ์ดํดํ๋ค! ChatGPT๊ฐ '์ปคํผ์ ์ถ์ฒํด์ค'๋ผ๊ณ ๋ฌผ์ผ๋ฉด ์ "์๋ฉ๋ฆฌ์นด๋ ธ๊ฐ ๋ง์๋ ์นดํ"๋ฅผ ์ฒ์ฒ ์ฐพ์๋ผ๊น? ๋น๋ฐ์ ๋ฐ๋ก ๋ฒกํฐ ๋ฐ์ดํฐ๋ฒ ์ด์ค(Vector DB)์ด๋ค. ์ ํต ๋ฐ์ดํฐ๋ฒ ์ด์ค๊ฐ '์ ํํ ์ผ์น'๋ฅผ ์ฐพ๋๋ค๋ฉด, ๋ฒกํฐ DB๋ '์๋ฏธ๊ฐ ๋น์ทํ' ๋ฐ์ดํฐ๋ฅผ ์ฐพ์์ฃผ๋ ํ์ ์ ์ธ ๊ธฐ์ ์ด๋ค. ๋ฒกํฐ ๊ฒ์, ์๋ฒ ๋ฉ(Embedding), ์ฝ์ฌ์ธ ์ ์ฌ๋, ์ ํด๋ฆฌ๋ ๊ฑฐ๋ฆฌ, ๊ทธ๋ฆฌ๊ณ HNSW, IVF ๊ฐ์ ์ธ๋ฑ์ฑ ์๊ณ ๋ฆฌ์ฆ๊น์ง! ๊ด๋ฆฌํ Pinecone๋ถํฐ ๋๊ท๋ชจ Milvus, ๊ณ ์ฑ๋ฅ Qdrant๊น์ง ๋ค์ํ ๋ฒกํฐ DB์ ์ฐจ์ด๋ ์๊ฐํ๋ค. AI์ ํ์ ๋๊ตฌ์ธ ๋ฒกํฐ DB๊ฐ ์ด๋ป๊ฒ ์ถ์ฒ ์์คํ , ์ด์ ํ์ง, RAG(๊ฒ์ ์ฆ๊ฐ ์์ฑ)์ ํ์ฉ๋๋์ง ์์๋ณด์. ๊ธฐ์ ์ ๋ฏธ๋์ ํ ๊ฑธ์ ๋ ๊ฐ๊น์์ง๋ ๊ธฐํ! ์์ธํ ๋ด์ฉ์ ์ฌ๊ธฐ๋ฅผ ํ์ธํด๋ณด์: https://doyouknow.kr/436/vector-database-guide-embedding-similarity-search-hnsw-ivf-pinecone-milvus/ ์ฌ๋ฌ๋ถ์ AI๊ฐ ์ถ์ฒํ๋ ์ปคํผ์, ์ด๋ค ๊ธฐ์ค์ผ๋ก ์ ํํ๊ณ ์๋์? ์๊ฒฌ ๊ณต์ ๋ ํ์ํฉ๋๋ค! โโจ #๋ฒกํฐ๋ฐ์ดํฐ๋ฒ ์ด์ค #AI #์๋ฒ ๋ฉ #์ถ์ฒ์์คํ #์ ์ฌ๋๊ฒ์ Read the full article
Vectors - Explained
A simple introduction to vectors covering: vector definition and representation, vector magnitude and direction, addition and subtraction of vectors, components of a vector, unit vectors, and the dot product of two vectors.
An introduction to vectors convering vector definition and representation, vector magnitude, scalar multiplication, vectors addition and sub

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ํ ์ ์ด ์ผ๊ฐํ ๋ด๋ถ์ ์๋์ง๋ฅผ ์ฒดํฌํ๊ธฐ
ํ ์ ์ด ์ผ๊ฐํ ๋ด๋ถ์ ์๋์ง๋ฅผย ์ฒดํฌํ๊ธฐ
ํ๋ฉด์ขํ์์ ์์์ ์ P(px, py) ๊ฐ ์ธ ์ A(ax, ay), B(bx, by), C(cx, cy)๋ก ์ด๋ฃจ์ด์ง ์ผ๊ฐํ ๋ด๋ถ์ ์๋์ง ์ธ๋ถ์ ์๋์ง๋ฅผ ํ๋จํ๋ ์ฝ๋๋ฅผ ์์ฑํด๋ณด์. ์ด๊ฑฐ ๋ง์น ๋ฌด์จ ๊ณ ๋ฑํ๊ต ์ํ๋ฌธ์ ๊ฐ์๋ฐ, ์ฌ์ค ๊ณ ๋ฑํ๊ต ์ํ ๋ฌธ์ ๋ง๋คโฆ
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MIT has a new chip to make AI faster and more efficient on smartphones
MIT has a new chip to make AI faster and more efficient onย smartphones
Just one day after MIT revealed that some of its researchers had created a super low-power chip to handle encryption, the institute is back with a neural network chip that reduces power consumption by 95 percent. This feature makes them ideal for battery-powered gadgets like mobile phones and tablets to take advantage of more complex neural networking systems. Neural networks are made up of lotsโฆ
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Word co-occurrence matrix and Words Similarity