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## Main Question or Discussion Point

I'm doing some work with vectors, and essentially, I have two vectors: a large vector and a unit vector pointing in a different direction. I would like to decompose the large vector into the components that are in the direction of and perpendicular to the unit vector.

This is in three dimensions, and shouldn't be too hard using cos and acos. However, this is for some computer work, where cos and acos are expensive -- is there any better way to do this using purely vector math (such as cross product, etc) or some other method not quite so expensive?

This is in three dimensions, and shouldn't be too hard using cos and acos. However, this is for some computer work, where cos and acos are expensive -- is there any better way to do this using purely vector math (such as cross product, etc) or some other method not quite so expensive?