Page 67 - Math SL HB Sem 2

Kolej MARA Seremban Mathematics IB High Level
Core : Vectors

Unit Vectors

Any vectors of magnitude I wit is a unit vector.

a The unit vector of a vector a is a vector whose magnifude
is 1 unit in the direction of a.
:1 a
a The unit vector ofa, a
t4

Zero vectors

For any non-zero vector a, lal>0 Zero vector is written as 0
a+Ca):(a)+a:0

Vectors In Coordinate System

For the moment we shall restrict the discussion to the vectors in 2-dimensional space (the
plane). Consider the Cartesianl-ry plane consisting of an origin O and a pair of
perpendicular vectors.
v

The two are the unit vector i in the positive direction ofthe
x-axis and the unit vector j in the positive direction ofthe
y-axis.
J
x
o I

v IfA is the point with coordinate (3 4) ,
,
A(3 ,4)
-+
3i+4j oN:3 so ON :3i
-)
NA=4 , so NA :4j
4i
--) ) -+
Therefore , OA : ON + NA :3i + 4j
x
o 3iN ie. the position vector ofA(3 , 4) is r:3i+4j

Similarly, the position vector of any point P(a , 6) is ai + bj.

Component of a vector, column representation

, =(v'\=,,i+ u,j
\u,)