12. A force acts at point A as shown. Determine the mean and standard deviation of this force acting at A using its x, y, and z components.

Solution

Force is shown in the following figure.

The direction of this F vector, u, is determined from the position vector r, which extends from A to B. The position vector r is given by

The magnitude of r, which represents the cord length AB, is

The unit vector is then

We know , then

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