Vectors represent both the magnitude and direction of a quantity, while scalars represent only magnitude. There are different methods for adding vectors depending on whether their directions are the same, opposite, or neither. The parallelogram rule is used to add vectors that are not in the same line, by transferring one vector to the end of the other while maintaining its position and magnitude, then drawing the resulting force. Pythagoras' theorem can also be used to calculate the magnitude of resulting vectors at right angles.

1. Vectors
Ms. Juanita Larraín-Linton

2. Scalars and Vectors
SCALAR
-Refers to a
MAGNITUDE...
Example: Speed
10 m/s

3. Scalars and Vectors
VECTOR
-Refers to a MAGNITUDE
AND ITS DIRECTION...
Example: Velocity
10 m/s South

4. Example
Mass
Ammount
of matter
Weight
(Force)
Attraction
of an
ammount
of matter
to the Earth
Scalar: 150 Kg Vector: 1500 N

5. ADDING SCALARS
Scalars only refer to QUANTITIES only:
We must add these quantities as numbers:
+ +
0.5 L + 0.5 L + 0.5 L 1.5 L

6. ADDING VECTORS
Vectors refer to both QUANTITIES and DIRECTION:
We must add them both....
HOW?

7. If both vectors are in the same
line....
10 N + 4N
14N

8. If both vectors are in the same line
but opposite....
10 N + 4N
6N

9. The parallelogram rule
If two vectors are NOT in the same line we
must apply this rule.

10. The parallelogram rule
1. “Transfer” your vector to the end of the other vector. It MUST have
the same position (angle) and magnitude (length).
1. Draw your the resulting force.

11. Pythagoras’ theorem: right angles
For all other
cases,
drawing
and measuring
angles and
lenghts is
required
30 N
40 N
50 N

12. Inclined surfaces