1. Vectors and Scalars – Learning Outcomes
Distinguish between scalars and vectors.
Recognise quantities as either scalars or vectors.
HL: Find the resultant of perpendicular vectors.
HL: Describe how to find the resultant of two vectors.
HL: Resolve co-planar vectors.
HL: Solve problems about vector addition and resolution.

2. Differentiate between scalars and vectors
Scalars are quantities with magnitude only, e.g.
distance,
time,
speed,
temperature,
mass,
For scalars, only magnitude matters.

3. Differentiate between scalars and vectors
Vectors are quantities with magnitude AND direction, e.g.
displacement,
velocity,
acceleration,
force
For vectors, both magnitude and direction both matter.

4. Differentiate between scalars and vectors
The distance between Dublin and Cork depends on the route you take.
The displacement from Dublin to Cork is constant, has a particular direction, and is different to the displacement from Cork to Dublin.

5. Recognise Quantities as Scalars or Vectors
State whether the following are scalars or vectors:
energy
width
area
weight
thrust
frequency
volume

6. HL: Find the Resultant of ⊥ Vectors
There are two rules for adding vectors.
If the vectors are head to tail, the resultant starts at the tail of one vector and ends at the head of the other vector.

7. HL: Find the Resultant of ⊥ Vectors
If the vectors are tail to tail, the resultant is formed from the diagonal of a parallelogram made from those two vectors.

8. HL: Find the Resultant of ⊥ Vectors
In either case, we get a right-angled triangle.
Thus, we can use trig rules to find resultants (Pythagoras’ theorem, sine, cosine, tangent).
e.g. Two forces are applied to a body, as shown. What is the magnitude of the resultant force acting on the body?

9. HL: Find the Resultant of ⊥ Vectors
e.g. A horse undergoes displacement of 3 km East followed by a displacement of 5 km North.
Draw a diagram showing the horse’s path.
What is the overall displacement of the horse from its starting point?
e.g. A ship moves parallel to a straight river bank at 4 m∙s-1. Bronagh walks across the ship at right angles to the direction of forward motion of the ship at 3 m∙s-1. Find Bronagh’s overall velocity as she walks.

10. HL: Describe How to Find the Resultant of Two Vectors
Attach strings to three force meters and tie the ends of the strings together.
Pull on the three force meters until the string knot is at rest.
The resultant of any two forces has magnitude equal to the third force and opposite direction.

11. HL: Resolve Co-Planar Vectors
If we are given a resultant vector, we can resolve the vector into its components using trigonometry.
e.g. The vector shown points East 30o North. Find its components in the East and North directions.

12. HL: Resolve Co-Planar Vectors
e.g. Find the vertical and horizontal components of a vector of magnitude 20 N acting at 60o to the horizontal.
e.g. Michelle pulls a rope which is tied to a cart with a force 300 N. The rope makes an angle of 20o to the horizontal. Find the effective vertical and horizontal forces on the cart due to the rope.