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I need to get $\Theta$ vector of weights for hyperplane in 3D that cuts off a single corner of a cube [1, 1, 1]. Cube's first corner is the origin. Or better to say I need to find a hyperplane that is tangent to a cube corner [1, 1, 1].

I am not strong in math to know how to do it. In fact, I never really worked on constructing hyperplanes. So not sure how to go about it.

EDIT: correct me if I am wrong, but I guess this question could also be stated as "constructing a hyperplane that is normal to a vector [1,1,1] and passes through point [1,1,1]"

Thank you

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If a cube is centered at the origin, and t is some given real number, the hyperplane $x+y+z=t$ either misses the cube entirely, or separates a corner from the cube.

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