1. Using Vectors

2. Two Displacements
A hiker walks east from camp for 2.0 km, then northeast for 3.0 km. What is the final displacement of the hiker?
Each individual displacement is a vector that can be represented by an arrow.
3.0 km
2.0 km

3. Graphical Addition The two vectors can be added graphically.
The tail of the second vector is placed at the tip of the first.
The length and directions are kept the same.
The result is the total displacement. It can be measured directly.
4.6 km
3.0 km
2.0 km

4. Commutative Property
Vectors can be shifted as long as they don’t change direction and magnitude.
Vectors can be added in reverse order and get the same result.

5. Parallelogram
If two vectors are added from a common origin one can be shifted to make a parallelogram.
This is the same as putting the tail to the tip.

6. Parallel and Antiparallel
Vectors that point in the same direction are parallel.
Vectors that point in opposite directions are antiparallel.

7. Cancellation
What happens if we add two antiparallel vectors of equal magnitude?
The vector sum is a zero length vector. The vectors cancel out.

8. Vector Subtraction
To subtract one vector, add the antiparallel vector instead.

9. Vector Triangles
Three vectors have the same magnitude, L, and form an equilateral triangle.
Find
They are already tip to tail, so
Find
Redraw the picture
The direction is up
The magnitude is
60o
Lsin60
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