__Category__: Algebra, Physics, Mechanics"Published in Newark, California, USA"

Find the centroid of the following weights: 2 lbs at (3, 0, 1), 5 lbs at (-2, 3, 2), and 9 lbs at (4, 1, 4).

__Solution__:

To illustrate the problem, it is better to draw the figure as follows

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The total weight of the three weights is

The x value of the centroid is calculated as follows

The y value of the centroid is calculated as follows

The z value of the centroid is calculated as follows

Therefore, the centroid of the three weights is