Page 65 - Math SL HB Sem 2

Kolej MARA Seremban
Mathematics IB High Level
Core : Vectors
VECTORS

5.1 Vectors In Trvo And s

Many physical quantities such as area, mass and temperature are completely described once the
magnitude of the quantity is given. such quantities aie called scarar.- oihei phy.,""I q;;;1i;;,
called vector are completely determin€d w_hen both a magnitude and a direction ;" .p""ii;J. i.;.
example, wind movement is usually described by giving ihe speed and the direction, i^y io *^pn
-
north. Other examples of vectors are force and accelerati,on_
Vectors Representation

Vectors may be represented by usin g directed line segments or arrows -
The magnitude ofa vector is represented by its length and its direction is given by the
direction ofthe arrow-

The tail of the arrow is called the initial point of ihe vector and the he ad of the anow tIrc terminal
point.

A
-+ )
This vector from O to A is written OA or OA or a or a.
a

o
Equal'Vectors

a Two vectors are equal if they have the same magnitude and
b the same direction .

Negative Vectors

a
Ifa is any nonzero vector, then
a
- , the negative ofa is
defrned to be the vector having the same magnitude as a
.A
but oppositely directed.

Addition Of Vectors

If a and b are any two vectors, then the sum a* b is the vector determined as follows :

Position the vector b so that its initial point coincides with the terminal point of a. The
vector a t b is represented by the arrow from the initial point ofa to the terminal point of
b.