Page 66 - Math SL HB Sem 2
P. 66
Kolej MARA Seremban Mathematics IB High Level
Core : Yectors
b b
a
a a+b a b;-a
b
From the right figure, it is evident that a + b = b + a, and the sum coincides with the
diagonal of the parallelogram when the two vectors are positioned so they have the same
initial point.
Subtraction Of Vectors
If a and b are any two vectors, then the dffirence of b from a is defined by
a-b:a+(-b).
Toobtainthedifferencea-bwithoutconstructing-b,positionaandbsotheirinitial
point coincide. The vector from the terminal point of b to the terminal point of a is then the
-
vector a b.
a
a- a a-b
-b b b
Scalar Multiplication Of Vectors
Ifa is a vector and 1" is a nonzero real number ( scalar ),
a ther, the product Xa is a vector whose length is I ?" I ti-"s
I
2a - -a the length of a and the direction is the same as a if 1" > 0
2
and opposite to that ofa if l, < 0.
Position Vector
A
--t
OA is called the position vector of A relative to the origin.
a Vectors such as a which is not related to a fixed position
are known as free vectors.
o
