Addition Example
Q: Billy Bob Joe starts going to school from his house. First he walks north 300m to the bus stop, and then the bus takes him 1km west to school.a) How far is Mr. Joe from his house when he is at school?
b) When Mr. Joe returns home what will his displacement be?
c) How will Mr. Joe’s displacement be affected if he took a different route to school?
A: First lets draw our situation with vectors. Assuming north is up ( when in doubt draw the north arrow ) we draw Mr. Joe’s northernly walk and then his westerly ride – a vector going up and a vector going left.
The blue line is the resultant displacement – the final position which Billy Bob Joe has, the tail of the 
vector is at the house, and its head is at the school.
a) Our vector addition turned out to be a right angle triangle, and is the hypotenuse. Lets use the pythagorean theorem to find out just how far Mr. Joe is.
300І x 1000І = | |І
| | = 1044m
Mr. Joe is 1044 metres from his home.
Notice that we have used the absolute value notation | | so that we can use the magnitude of without its direction.
b) When Billy Bob Joe returns home his displacement will be zero, he is zero metres away from his home.
c) Taking an alternate route would not change Mr. Joe’s displacement, he would still end up in his school. Unlike distance, the displacement is not affected by how you got to a place, its only concerned with the location of that place.