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.
1
Differentiate between scalars and vectors
Scalars are quantities with magnitude only, e.g.
distance,
time,
speed,
temperature,
mass,
For scalars, only magnitude matters.
2
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.
3
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.
4
Recognise Quantities as Scalars or Vectors
State whether the following are scalars or vectors:
1. energy
2. width
3. area
4. weight
5. thrust
6. frequency
7. volume
5
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.
6
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.
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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?
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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.
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HL: Describe How to Find the Resultant
of Two Vectors1. Attach strings to three
force meters and tie
the ends of the strings
together.
2. Pull on the three force
meters until the string
knot is at rest.
3. The resultant of any two
forces has magnitude
equal to the third force
and opposite direction.
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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.
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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.
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