(a) In Example 1, show that the line segment connecting ((1 / 2,0,1 / 2)) and ((1...

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(a) In Example 1, show that the line segment connecting \((1 / 2,0,1 / 2)\) and \((1 / 2,1 / 2,0)\) is entirely in the triangular region.

(b) Is the point \((1 / 2,1 / 8,3 / 8)\) on this segment?

(c) Under what conditions on \(x_{2}\) and \(x_{3}\) is the point ( \(\left.1 / 2, x_{2}, x_{3}\right)\) on this segment?

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