Geometric proof of vector dot product

dotProof Source: colorful introduction to Linear Algebra (may 2014) Cosine Similarity – understanding it as volume of parallelepiped cosineSimilarity Another good source for understanding dot product : dot_product_components dot_product_rotation

other resources:

Significance &Application of Cross product and Dot product.

Independence of  Perpendicular components of the motion

Math Insight:

\frac{a\cdot b}{\left \| a\right \|}= cos\alpha \left \| b \right \|

“projection” of vector b on a equals cosine of angle between them times the length of b or vice versa projection of a on b:


Dot product Identities, some pictures taken from



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