IR >
1132 is the set of ordered pairs of real numbers
Formally , IR '
For example, ( 3, 1) f- ( 1,3) y '' ( 1,3) • This visual
( 3, I )
More generally , lRn={ (a . . . . . . an) : a. . . . . ,anElR)
IR " "
Formally , 1133 = { (a , b , c ) : a. b. c EIR} I
ordered triple
1133=1 Ca , b. c ) : a. b. c. c- IR} Z
-x (o-0,0)
of IR ' is called
Graphingequations 2
y = x ±
y Pz : (Xz , Yz ) N •Bo
of¥""ix IP , Pzl = (Xz- X , ) 't (yz -y , )
"
= I Pap , I
Distance between points in three space IRS Qa -_ (Xz ,Yz , Zz)
00
" ""' %|o#• . """ "⇒
(X, ,Y , ,Z ,)/ ¥ to you
Distance between points in three space IRS QE (Xz ,Yz , Zz)
What you see •.
-
'
Y f. --
ix. i.%,
f- x ¥ .
×
.
Equation of a sphere A sphere of radius r and center (xoxo ,Zo)
is represented by the equation ( x - Xo)! Cy - yo)'t Cz -Zo)2=rZ
If (x.y , z) satisfies this equation ,
then it is at distance r away from
( Xo -Yo , Zo)
-
- 4ytz '
-22--100=0
is the eq of a sphere and find the radiuskente r.
'
'
Regions defined by multiple inequalities I E Y E 2 ,
X EO l E Z E Z
Z
all constraints x
Regions defined by multiple inequalities 4 Ex't y 't Es ai
E
L
Regions defined by multiple inequalities Z
4 E X't y 't Es 9 a
Z E O ± ¥
Moral : must satisfy by z e - I ) all constraints