Vectors

A Sense of Direction by flickr user Scuddr

Identify each of the following quantities as scalar or vector.

(g) The boat was headed N42°W across the lake.

(h) The tires were worn out after 120 000 kilometres of driving to and from work.

(f) Jess jogged six blocks west along Portage Avenue.

(e) Jeff was driving at 100 km/h for 40 minutes.

(d) There are 24 students in math class.

(c) Today we had a 30 km/h north wind.

(b) The airplane flew 515 km/h at a bearing of 315°.

(a) There are five people living in the house just north of yours.

scalar vector

vector scalar

vector

vector

scalarscalar

vector

vector

VectorsVector: A quantity that has both a magnitude and a direction.

4 Notations for Writing a Vector

(1) An arrow• length indicates magnitude.• tip indicates direction.

(4) [angle] [direction] of [direction](3) [direction] [angle] [direction]

(2) Bearings: Angle is always measured clockwise from North. Angle is always written as a three digit number.

4 Notations for Writing a Vector

(1) An arrow• length indicates magnitude.• tip indicates direction.

Note: All of the above examples indicate the same vector.

3cm1cm = 10km

60°

(2) Bearings: Angle is always measured clockwise from North. Angle is always written as a three digit number.

4 Notations for Writing a Vector

Note: All of the above examples indicate the same vector.

(3) [direction] [angle] [direction] (2) [angle] [direction] of [direction]

3cm1cm = 10km

60°

State the direction of each vector in five ways.

ABCD is a parallelogram with AD = DE. Each segment in the diagram is a vector. Answer the following questions.

(d) Name a vector that is parallel to but not equal to EA or EB

(c) Name a vector that is collinear with BA

(b) Name a vector that is the opposite of AB

(a) Name a vector that is equal to AD

HOMEWORK

State the magnitude and direction of each vector.

HOMEWORK

State the magnitude and direction of each vector. (You can determine the answer using ruler and protractor.)

HOMEWORK

Draw scale diagrams of the following vectors using pencil, ruler, protractor, and paper. Label the diagram. Be sure to indicate the scale you used.

(b) A boat is headed 300° at 45 km/h.

(a) Tiffany walks 13 blocks in a direction E15°S.HOMEWORK