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Converting movement vector to dir vector and magnitude

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How would you convert a movement vector to a directional vector and a magnitude (speed)? I know just normalizing it would give you the directional vector, but how would you extract the speed out of it? Thanks in advance

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For a 3D vector

magnitude = sqrt(x*x + y*y + z*z);

Drop the z*z for a 2D vector, add a w*w for a 4D vector. This extends to any number of dimensions.

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