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# dot product of unit vectors

Hi

This is a bit of a basic question but i was just wondering out of curiosity.

Take i and j as unit vectors. What is i.i and j.j? The answer in both cases is 1. Is this because  you assumed the 2 vectors were on top of each other and so had an ange between then of 0 degrees so the dot product = |i|.|i| . cos(0) = 1

thanks
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andieje
1 Solution

Commented:
I see you are using the formula v1 . v2 = |v1| |v2| cos (theta), where theta is the angle between v1 and v2.So, if you take the dot product of any two vectors (unit or not) that are pointing in the same direction (i.e., they are parallel), then the angle between them is 0 degrees. v1 . v2 = |v1| |v2| cos (0) =  |v1| |v2| In your case v1 and v2 are unit vectors so  |v1| |v2| = 1*1 = 1If v1 and v2 were parallel, but in opposite directions, then theta = 180 degrees, then v1 . v2 = |v1| |v2| cos (180) =  -|v1| |v2|
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Author Commented:
thanks
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