A man walks 18.5 km west, 24.0 km at 30 degrees northwest and then 12.0 km north. Show that the order of adding the vectors does not affect the resultant (to demonstrate make two diagrams for this). What is his resultant displacement? What distance did he walk?

If you just do exactly what the instructions say, you'll see that it makes sense. Grab a piece of graph paper, and draw two diagrams. On the first one, start at a point and draw a vector 18.5 units to the west. Then from the tip of that vector, draw another vector 24 units long at 30 degrees northwest (which really means that it ends at a point units west and units north), and then finally draw your last vector from the tip of the previous one going 12 units north. The resultant will be the vector drawn from your starting point to the ending point of the last vector.

Now draw your second diagram, but this time mix up the order of the vectors. For example, first go north 12 units, then west 18.5 units, and finally 30 degrees northwest 24 units. If you draw the resultant this time, you'll find it's exactly the same as the previous diagram! It doesn't matter what order you draw the vectors in.

As far as the last two questions go, the second one is easy: He didn't walk in a straight line, so the total distance he walked was 18.5 + 24 + 12 = 54.5 km. The resultant displacement, however, is the straight-line distance between the start and the finish. To calculate that, you'll need to add up the total westward distance that he traveled (18.5 + km), along with the total northward distance (12 + 12 km). Then use the distance formula () to find the resultant.