MATH1131 Lecture Notes - Lecture 2: Unit Vector, Bromine, Tibet
3 Jun 2018
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Department
Course
Professor
I
&0.([)
rfrit
' :-
-13
In other words, addition ancl scalar multiplication is done
component wise.
Exampre 1.r8. Lqt v: (l)-: (;) . u,
Findv*w,3w.
I+r=().ti)= (l)*
3E =, r(',) " (l) n
Exercise L.17. Give alge,braic. ve.c.tor proerfs of the fol-
lowing laws of arithinetic for two ditrensional spaee:
(a+b)f c: a* (b+ c) assoclative law
a+b: b+a couunntatir,e law
t(a + b) : ta + tb distributive Iaw
L* A, L eR. , ihn t= (t) , i.([) . fo,
{+t = (?:1il " (lii:)- !+{
$ng a,,or, br, En rrr t(.}
ar, (l) anl A-(-;)
Jmcr &=. (i1 -r6'e, fl,r vgr&r rr f^*\rl
1,2 Algebraic vectors
Okay, now put yotu crayons away.
So far we have worked without reference to a ceordinate
system. Introducing a co-ordinate system allows us to see
vectors as algebraic objects. We are obliged to specify the
dimension when working with a. coordiuate system.
A1En three dirnensionai space i" tG
Qwhere 1 is thc u-component, 2 is the g-component
qnd 3 io the z-component.
o
fiir)
ffi)
o"a. 1 . (ii)
rlnrn drrr. fi *{i^s
$eu A'c . t-r - (Li)
u'r=(ii) .*(It*)
= f ii'...iT'\
[r, * {u,/
= *(r*11
-rJ
-ie8 u
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1.16. Let A, B be two points in three di-
ftce and lel M he their midpoin t,. Firrl- Ort
1.3 Basic concepts regarding vectors
in lRn.
Recall the following very importa,nt resr-ilt:
.J
AB:OB_OA
where -4, B are points in lR" and Q is the origin.'
Example 1.18. Suppose A : P,-1,2] and B :
[1,5, -3] are two points in m.3. rinA Al..
;* i'c =o'g -ia
^HJ* =H)-(l
Exampre l.r,e. Jrl# I : l?,-i,21 anrr B :
14,-2,4)are two points in R3. Is Oi 1>u'allr:l tn OBI
I-/
Lrt ie * e.. ( ii)
Ge.ometrica.lly,
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