Vectors

24

Contents:

A Directed line segment representation [5.1, 5.3]

B Vector equality [5.1, 5.2]

C Vector addition [5.2]

D Vector subtraction [5.2]

E Vectors in component form [5.1 - 5.3]

F Scalar multiplication [5.2]

G Parallel vectors [5.1, 5.2]

H Vectors in geometry [5.2]

Opening problem #endboxedheading

Holger can kayak in calm water at a speed of 20 km/h.

However, today he needs to kayak directly across a

river in which the water is flowing at a constant speed

of 10 km/h to his right.

Things to think about:

² What effect does the current in the river have on

the speed and direction in which Holger kayaks?

² How can we accurately find the speed and direction that Holger will travel if he tries to kayak

directly across the river?

² In what direction must Holger face so that he kayaks directly across the river?

VECTORS AND SCALARS

To solve questions like those in theOpening Problem, we need to examine thesizeormagnitudeof the

quantities under consideration as well as thedirectionin which they are acting.

To achieve this we use quantities calledvectorswhich have both size or magnitude and also direction.

Quantities which only have magnitude are calledscalars.

Quantities which have both magnitude and direction are calledvectors.

For example,velocityis a vector since it deals with speed (a scalar) in a particular direction.

Other examples of vector quantities are acceleration, force, displacement, and momentum.

IGCSE01

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_24\483IGCSE01_24.CDR Monday, 27 October 2008 2:25:07 PM PETER