This is just to say that I don't think choosing the vectors with the maximum Euclidean norm will
suffice. In the example below, the two longest vectors (red) are collinear, and the hull derived from
them—regardless of $c$—will be a line segment, which cannot contain the original (green) points.
Hull Vectors http://cs.smith.edu/~orourke/MathOverflow/HullVectorsCex.jpg
This is just to say that I don't think choosing the vectors with the maximum Euclidean norm will
suffice. In the example below, the two longest vectors (red) are collinear, and the hull derived from
them—regardless of $c$—will be a line segment, which cannot contain the original (green) points.
Hull Vectors http://cs.smith.edu/~orourke/MathOverflow/HullVectorsCex.jpg
This is just to say that I don't think choosing the vectors with the maximum Euclidean norm will
suffice. In the example below, the two longest vectors (red) are collinear, and the hull derived from
them—regardless of $c$—will be a line segment, which cannot contain the original (green) points.