Source: colorful introduction to Linear Algebra (may 2014) Cosine Similarity – understanding it as volume of parallelepiped Another good source for understanding dot product : http://betterexplained.com/articles/vector-calculus-understanding-the-dot-product/

other resources:

Significance &Application of Cross product and Dot product. http://visualizingmathsandphysics.blogspot.cz/2013/06/vectors-significance-of-cross-product.html

Independence of  Perpendicular components of the motion http://www.physicsclassroom.com/Class/vectors/u3l1g.cfm

Math Insight: http://mathinsight.org/dot_product

$latex \frac{a\cdot b}{\left \| a\right \|}= cos\alpha \left \| b \right \| &s=4$

“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 http://gamemath.com/