Suppose you're a camel on a large flat plane, and start out 1 mile
east of Timbuktu and 2 miles north. You trot for an hour and then
find that you're 4 miles east and 6 miles north. You're average
velocity in the west-east direction is (4-1) miles per hour which equals
3 miles per hour. Your average velocity in the south-north direction is
(6-2) miles per hour which equals 4 miles per hour. This is your
average velocity. In terms of vectors, you could define an x-y
coordinate system with its origin in Timbuktu oriented so that the
x axis was west-east. Then you could write the average velocity in
vector form as 
. The speed of the
camel is then just 
.
More formally we can denote the final position of the camel by the
vector 
and the initial position by the vector 
.
Then in analogy to eq. 3.1 we have
We can write this in terms of components as
