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.
The Tools of the Trade: Some Trigonometric Equations ...
The Pythagorean Theorem The Sine Law
A c b
b a C
B a C
SAS The Cosine Law SSS
B a C
Some Useful Properties of Angles ...
When two lines intersect, the angles opposite
each other at the point of intersection are
Angles on alternate sides of a transversal are
Angles on coresponding sides of a transversal
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.
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 ...
A cyclist is traveling at 10 m/s. He has a tailwind of 0.5 m/s.
What is his overall velocity?
The Triangle Method ...
We use the triangle method when the vectors are arranged tiptotail.
11.7 cm 59° S of E
Scale: 1 cm = 2 km
23.4 km 59° S of E
Remember, we use measurements with a ruler and protractor to find
The Parallelogram Method......
We use the parallelogram method when the vectors are arranged
tail to tail.
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.