Collinear Vectors:

Collinear vectors act along the same line or axis: East - West or North - South.
When adding collinear vectors one must ensure that they are all pointing in the same direction.

The general rule for adding collinear vectors is: "add vectors from tail to head".   In other words from the tail of the first vector to the head of the last.

noteIf two vectors point in opposite direction you must reverse the direction of one of the vectors.  

noteWhen you change the direction of a vector you must also change the sign in front of the magnitude of the vector.


Example: Mr. Forget drives 5.0 km East from home to a gas station and then back West to the local bakery for another 2.0 km.  What is Mr. Forget's total displacement?


d1 = 5.0 km [E]
d2 = 2.0 km [E] = -2.0 km [W] 

noteNote we switched 2.0 Km [E] to 2.0 km [W] by changing both its direction and its sign from "+" to "-"

Find: dt    

Solution:   dt  d1 + d= 5.0 km [E] + (-2.0 km [W] ) = 3.0  km [E]
notePlease note that the total distance travelled by Mr. Forget would  be 7.0 km because distance does not take into account the direction of travel.