Page 71 - Math SL HB Sem 2

Kolej MAL{ Seremban Mathematics IB High Level
Core! : Veciors

:(a.
4) m (a.b) = (za). b b)zr
5) a.[= I"llUIif and only if a parallel to b
a . b : - | a I I u I if onty if a and b in opposite direction.
"na
6) a, b = 0 if and only ifa is perpendicular to b

Proo f

,
5) Ifvectorsaandaparallel the angle between a and b are 00 or 1800.
:
So,a.b: I I allnl
"lltlcoso"
b a
or, a. [: lallul"ostso" =-lalltl 0:1800

b a

6) If vectors a and b are perpendicular the angle between a and b is 90o so,
a.n: lallblcosgOo = 0 b

a
The scalar product between a and b is also defined

a.b = a1b1+aZbZ+a3b3

ErseJ

Known that i, j, and k are perpendicular and the angle of two vectors is zero if it parellel.
So,
6 = (ari + ai + a3k). (bi+ bi + Uk)
". )+a163(i. k) +a2b1(j .i) + a2b2Q. j )+ orDr(i. k)+
= aftli.i) + a1b2(i. j
)
a3b1(k. i + a3b2(k. j) + a:6:(t. t< )
known that,

i.i:j.j:k.k =1 and j.i:j.k=k.j:k.i =i.k:0 ,

.. a.b = a1b1+a2b2+a3b3