### Suppose you first walk 12.0 m in a direction 20º west of north and then 20.0 m in a direction 40.0º south of west. How far are you from your starting point, and what is the compass direction of a line connecting your starting point to your final position? (If you represent the two legs of the walk as vector displacements A and B , as in Figure 3.56, then this problem finds their sum R=A+B.)

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**SOLUTION:**

First, we solve for the *x* and *y* components of vectors A and B.

For vector A, the components are:

For vector B, the components are:

Since we know the components, we can now solve for the resultant vector R by adding the components together.

The resultant of the x-components is:

The resultant of the y-components is:

The magnitude of the resultant can be solved using the Pythagorean Theorem. That is:

The compass direction is

The compass direction is .