Class notes
Chapter 12 Class notes CALC. 3 003
- Course
- CALC. 3 003
- Institution
- University Of Akron
Detailed and organized class notes over the chapter 12
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Chapter 12.1 xyz space HialtalebAssign 12.1Recall Xy Plane 122 rectleartesian Note
New xyz space
4 1
Recall a
IT se
set ofpointsxyzwhere z 1 x y areanything
is a plane parallel to x y planewhich
crosses z axis at 2 1
Simularlywegetplanesfrom or
no Fortinate
plane
4 0 Xz coordinateplane
2 0 XY coordinateplane
distanceform
so w n gk r roo
Recall dillx x.tt y y
ii it s
bw between
Therefore
distancebetween x y Z x in 123
yZ
d x t
y 4 2 Zz
XhtxlyKACZ.tl
h.k l is fixed in 123 r Let Eff yh.tl
Let roo
es r
seaygiif.to
, Ex show that x y 72 4 64 22 6 Step1 put into standardform
is the eq of a sphere findthecenter 2 Completethe sq
radius 3 identify
6 49 1
Formulas
Center 12 3 7 r V8 distanceform
xyplane d Nx x.tt y 4,7
xyz plane d Vix x.it yyzl'tCZ2,7
Chapter 12.2 Vectors
Vectors A 2vectorvector in Re is a pair of s written as I
A 3 vectorvector in Rs is atrippledof s as a ae a
Zero Vector is Q 20,07
Vectors a b are equal
I aa
is correspondingcomp are
a b an b I k
length
the length of a vector ca a is la If
the standardbasisvectors
Re 21,07 20,1
129 5210,0 20.1.07 A 1 20 0,17
3rectors
Vector operations
vectors
multiple vectors by s component wise
AKA S tipication
HIM
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