For some reason this is bothering me. Can anyone explain to me why if you take two vectors and multiply all the corresponding parts together and add them, that it's the same thing as multiplying their lengths together and multiplying that by the cosine of the angle between them?

I feel like I understood this at one point, but for some reason it just seems weird to me. But I should know this, because it is the simple definition of dot product.

Question

For some reason this is bothering me. Can anyone explain to me why if you take two vectors and multiply all the corresponding parts together and add them, that it's the same thing as multiplying their lengths together and multiplying that by the cosine of the angle between them? 

I feel like I understood this at one point, but for some reason it just seems weird to me. But I should know this, because it is the simple definition of dot product.

kainui · Answer

I know how to show this with algebra, but it's just not very convincing to me for some reason.

ikram002p · Answer

you wanna prove the dot product ?

anonymous · Answer

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