Worksheet1: Vectors
Because vectors have direction and magnitude, they have to be added in a different way than numbers do. For numbers we just add them as 1+1=2 or
7+8=15. For vectors this might not be true. For example if you travel 8 km east in one day and 10 km east the next day, at the end of two days you will be 18 km east of the point where you started.
WEST EAST
If on the other hand instead of going east 10 km you decide to go west 3 km, at the end of 2 days you will be 5 km east of the point where you started. This exemplifies the way vectors are summed: taking their direction into account.
NOTE: you always add vectors like arrows, “head to tail.”
WEST EAST
In the drawings above, the purple arrow represe nts the “result” of the addition of the vectors, the net displacement. We add and subtract them taking account of their direction. What happens when we also travel north and south?

QUESTION1 : What is the net displacement that corresponds to the drawing below? If you assume that each square is 1 km, and if we start from the tail of vector A, where do we end up? What is our net displacement?
NORTH
B
WEST A C EAST
SOUTH
QUESTION2 : What is the net displacement that corresponds to the drawing below?
NORTH
WEST A
B
C EAST
SOUTH

ANSWER1: We end up 4 squares (km) east. The figure below gives the resulting vector or displacement in red.
NORTH
WEST A
B
C EAST
SOUTH
Answer2: Following the same philosophy we end up 2 squares south. The net displacement, or the sum of the vectors is given by the red arrow.
NORTH
WEST A
B
C EAST
SOUTH