Discussion
The shortest distance from the point (-10,10,-10) to the z-axis, is
Answer: E
The shortest distance is \(10\sqrt{2}\).
The foot of the perpendicular from \((x, y, z)\) to the z-axis is \((0, 0, z)\), so the distance depends only on \(x\) and \(y\):
\[ d = \sqrt{x^{2} + y^{2}} = \sqrt{100 + 100} = 10\sqrt{2} \]
The option \(10\sqrt{3}\) is the distance from the origin, which wrongly includes the z-coordinate, and 10 is the distance to a coordinate plane rather than to the axis.
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