|
Review
of vectors
Clement Radcliffe,
Contributor
Last
week you were given solutions to past paper questions. I do hope that you found
them beneficial. You are expected, of course, to continue to do other examples
on your own. Past papers are available in the the bookshops and you should endeavour
to make use of these. We
begin to review of vectors. Please review the following descriptions: A
motor car travels with (a) a velocity of 45 km per hour due north, and (b) a force
of 25 N due east. Could
you say what both statements have in common? You are correct that in both cases,
their sizes and directions are given. These are examples of vector quantities,
representing velocity of a car and force respectively. A
vector quantity is one which identifies both the magnitude (size) and direction,
for example, velocity given above. A
speed of 20 metres per second is a scalar quantity. (No direction given). Vector
quantities are usually represented in the form: You
may illustrate this on your own, using the Cartesian diagram above as follows:
From the diagram A has coordinates (1, 2) and B (5,5) 
(c)
A vector  represented
by  may be placed anywhere
in the Cartesian diagram, as long as the x and y components are satisfied. These
would all be equal vectors with the same length and are in the same direction
and represented by 
In
this regard
 Please
attempt the following example: Example:
The vectors b and c are given in the diagram below. Express these
in the form  
Please
attempt the following for Homework. ,
a or
as a Column vector We
will review Vectors represented as Column vectors. The
vector =
if x and y are representively the x and y components of the line AB
on the Cartesian diagram. EXAMPLE 
Please
Express  in the form
If
your answer is  then
you are correct. Points
to note (a)
Avoid making the common error of interchanging x and y values. (b)
If the coordinates of A X1, Y1) and
B(X2, Y2) are given then x = x2
- x1 and
y = y2 - y 
Given
the following diagram which shows vectors b and
c. Express
in the form (i)
b
(ii)
c
(iii)
Plot on the graph the vectors (a) x =
(b) y
=  
Clement
Radcliffe is the principal of Glenmuir High School in May Pen. | 
