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In three dimensional space with gravity, one cuboid has an initial velocity relative to the other. Neither cuboid is rotating and they are both aligned to the axes. One of the cuboids is not moving relative to the origin(and is not affected by gravity). How to determine if they will collide?

My idea is to collide the travel paths of all the vertices of cuboid A with the surfaces of cuboid B and vice versa.

Is there a better way? If so, how? If my approach is flawed, what is the correct approach?

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    A cuboid of side $a$ centered at $A$ will collide a cuboid of side $b$ centered at $B$ if and only if a cuboild of side $0$ centered at $O$ will collide a cuboid of side $a+b$ centered at $B-A$. As long as the gravitation force is uniform, you can forget it too. – 2017-01-15
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    @achillehui I forgot to mention that one of them is not affected by gravity. Your comment seems to deal with only one particular moment in time, but the question is about if given infinite time and the initial velocity will they eventually collide – 2017-01-15
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    Cuboid vs. cube : what is the difference. – 2017-01-15
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    @JeanMarie cuboid = rectangular prism(that can be a cube). Long time ago in a forgotten question someone asked me if by "rectangular prism" I mean cuboid, I read the Wikipedia page and said yes, and have since used that term – 2017-01-15
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    @achillehui Actually, thank you. You just solved my problem – 2017-01-15

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