# Middle Vector

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I wonder how I most easily find the middle vector between two other given vectors? I illustrated it with a l33t drawing of mine :) http://www.mercenaries.ws/midvector.gif If I got the two black vectors, how will I find the grey?

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In case I didn't make myself clear: I want all three vectors to lie in the same plane.

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For the direction (if the two original vectors are a and b and the one in the middle is c):
c = a + b.
This is because the resulting vector of an addition is the diagonal of the parallelogram formed by the vectors a and b.

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but won't it be alot longer?

If I add two unit vectors, the result of that addition will not be a unit vector. Lets say 0/1/0 and 1/0/0 for simplicity¨s sake, result will be 1/1/0, and it will then have to be normalized to get the right length.

Is there any way to get around the normalization (and its sqrt())?

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One thing to note is that the situation is ambiguous if the vectors are opposite to each other. For example for up and down facing vectors, you could choose left or right facing vector to be the between vector.

The only way to avoid normalization that I can think of is using spherical coordinates. But that would probably end up being a lot more computation unless you already have the vectors in spherical coords.

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good point with the ambiguity *notes to back of head* :)

Thanx for the reply guys, big help.

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