1. Vectors
A Sense of Direction by ﬂickr user Scuddr
2. Identify each of the following quantities as scalar or vector.
vector
scalar
(e) Jeff was driving at
(a) There are ﬁve people living
100 km/h for 40 minutes.
in the house just north of yours.
scalar
vector
(f) Jess jogged six blocks
(b) The airplane ﬂew 515
west along Portage Avenue.
km/h at a bearing of 315°.
vector
vector
(c) Today we had a (g) The boat was headed
30 km/h north wind. N42°W across the lake.
vector vector
(d) There are 24 (h) The tires were worn out after 120 000
students in math class. kilometres of driving to and from work.
scalar
scalar
3. Vectors
Vector: A quantity that has both a magnitude and a direction.
4 Notations for Writing a Vector
(1) An arrow (2) Bearings: Angle is always
measured clockwise from North.
• length indicates magnitude.
Angle is always written as a three
• tip indicates direction.
digit number.
(3) [direction] [angle] [direction] (4) [angle] [direction] of [direction]
4. 4 Notations for Writing a Vector
(1) An arrow (2) Bearings: Angle is always
• length indicates magnitude. measured clockwise from North.
Angle is always written as a three
• tip indicates direction.
digit number.
1cm = 10km
60°
3cm
Note: All of the above examples indicate the same vector.
5. 4 Notations for Writing a Vector
(2) [angle] [direction] of [direction]
(3) [direction] [angle] [direction]
1cm = 10km
60°
3cm
Note: All of the above examples indicate the same vector.
6. State the direction of each vector in ﬁve ways.
7. ABCD is a parallelogram with AD = DE. Each
segment in the diagram is a vector. Answer the
following questions.
HOMEWORK
(a) Name a vector (b) Name a vector that
that is equal to AD is the opposite of AB
(d) Name a vector that is parallel
(c) Name a vector that
to but not equal to EA or EB
is collinear with BA
8. State the magnitude and direction of each vector.
HOMEWORK
9. HOMEWORK
State the magnitude and direction of each
vector. (You can determine the answer using ruler and protractor.)
10. Draw scale diagrams of the following vectors using pencil,
ruler, protractor, and paper. Label the diagram. Be sure to
indicate the scale you used.
HOMEWORK
(a) Tiffany walks 13 blocks in a direction E15°S.
(b) A boat is headed 300° at 45 km/h.
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