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580. Let A = (4, 0, 0), B = (0, 3, 0), and C = (0, 0, 5). (a) Draw a diagram, then find coordinates for the point closest to C on segment AB. (b) Find the area of triangle ABC. (c) Find the length of the altitude drawn from A to BC.

580. Let $A=(4,0,0),B=(0,3,0)$, and $C=(0,0,5)$ (a) Draw a diagram, then find coordinates for the point closest to $C$ on segment $AB$. (b) Find the area of triangle $ABC$. (c) Find the length of the altitude drawn from $A$ to $BC$.