Cambridge Additional Mathematics

280 Vectors (Chapter 11)

Opening problem

An aeroplane in calm conditions is flying at 800 km h¡^1 due

east. A cold wind suddenly blows from the south-west at

35 km h¡^1 , pushing the aeroplane slightly off course.

Things to think about:

a How can we use an array of numbers to represent the

speedanddirection of the plane?

b What operation do we need to perform to find the effect of the wind on the aeroplane?

c Can you determine the resulting speed and direction of the aeroplane?

In theOpening Problem, the effect of the wind on the aeroplane is determined by both its speedandits

direction. The effect would be different if the wind was blowing against the aeroplane rather than from

behind it.

Quantities which have only magnitude are calledscalars.

Quantities which have both magnitude and direction are calledvectors.

Thespeedof the plane is a scalar. It describes its size or strength.

Thevelocityof the plane is a vector. It includes both its speed and also its direction.

Other examples of vector quantities are:

² acceleration ² force ² displacement ² momentum

For example, farmer Giles needs to remove a fence post. He starts

by pushing on the post sideways to loosen the ground. Giles has a

choice of how hard to push the post, and in which direction. The

force he applies is therefore a vector.

From previous courses, you should have seen how we can represent a vector quantity using adirected

line segmentorarrow. Thelength of the arrowrepresents the size or magnitude of the quantity, and the

arrowheadshows its direction.

POSITION VECTORS

Consider the vector from the origin O to the point A. We call this theposition vectorof point A.

² Thisposition vectorcould be represented by

¡!

OA or a

bold used in textbooks

or ¡!a.

used by students

² Themagnitudeorlengthcould be represented by

j

¡!

OAj or OA or jaj or j¡!aj.

A VECTORS AND SCALARS

a

O

A

cyan magenta yellow black

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_11\280CamAdd_11.cdr Friday, 4 April 2014 2:06:59 PM BRIAN