1. Vector Addition

2. Draw scale diagrams of the following vectors using pencil,
ruler, protractor, and paper. Label the diagram. Be sure to
indicate the scale you used.
(a) Venice walks 13 blocks in a direction E15°S.
(b) A boat is headed 300° at 45 km/h.

3. The Tools of the Trade: Some Trigonometric Equations ...
The Pythagorean Theorem The Sine Law
A
A c b
c B
b a C
B a C
SAS The Cosine Law SSS
A
c b
B a C

4. Some Useful Properties of Angles ...
Opposite Angles
When two lines intersect, the angles opposite
each other at the point of intersection are
a° congruent.
b° b°
a°
Alternate Angles
Angles on alternate sides of a transversal are
congruent.
a° b°
b° a°
Corresponding Angles
Angles on coresponding sides of a transversal
are congruent.
b° a°
b° a°

5. Adding Vectors Using Scale Diagrams ...
A vector is represented by an arrow. It's LENGTH determines it
MAGNITUDE and the TIP determines its DIRECTION.
When a vector is moved around in a
plane it is considered to be the same
vector. These two vectors are TAIL
considered to be identical:
Vectors can be added an any order.
TIP
When two vectors are added a new vector is made. It is
called the RESULTANT vector.
a means "vector a"
a means "magnitude of vector a"
There are two techniques that we use to add vectors using a
scale diagram ...

6. A cyclist is traveling at 10 m/s. He has a tailwind of 0.5 m/s.
What is his overall velocity?

7. The Triangle Method ...
We use the triangle method when the vectors are arranged tip­to­tail.
11.7 cm 59° S of E
6cm
Scale: 1 cm = 2 km
10cm
RESULTANT
23.4 km 59° S of E
RESULTANT
Remember, we use measurements with a ruler and protractor to find
the "answers."

8. The Parallelogram Method......
We use the parallelogram method when the vectors are arranged
tail ­ to ­ tail.

10. Peter drives 100 km/h at a bearing of 300 , then he turns 45 N
and travels at 50 km/h. Determine the resultant vector.

11. Page 318
Questions 1 ­ 8