what does the value of the dot product of two vectors tell us?
In: 10
The dot products tells you **how similar** and **how big** the two vectors are.
A dot product of 0 means that either the vectors have “nothing in common”, meaning they are orthogonal to one another, or one of the vector is 0.
If two vectors go exactly in the same direction, so they are as similar as they can possibly be, then the dot product is simply the multiplication of both lengths. More generally, if you increase the length of a vector, the dot product will increase proportionally.
If you’ve done some geometry, you probably know how important **angles** and **lengths** are. The dot product is combining those two notions into a single one, and while this might sound unintuitive, it does wonders for mathematical formula.
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