oMmddarygOetodba5a.rclass questions
hattieIIntroduced 2B 3D vectors
Vector addition Scalar maltHow to parametrize a 1 he
given point rector
I.IE dlppammtaieeegafoorLi
f Ctl Pt t E
ExerciseCIA parametrize the line starting
at 142,31 and pointingin the Cl 1,0 direction
2 Try to parameterize theline connecting 14,5 and2 2
O117 air is
a ioi
gs
L param hey 5 It 1213 slitt z t 31t.lt Ago
OrI g Q
ii I iP
L
Q P starts at P
points to Q
So L has egn
gt CI 22 t to 14,57 21 2
2 2 t t 12 3 f2t2t 243T
The egh for the linefetmeen.pk
Let P Q E IRB or 1122
be two pointsI yi
L L has parametricOa equation
P
Ip FH Pt E CQ P
If F Xi Yi Zi
and Q Xz yr Zz then
f Ct xitcxz x.lt yitcyz yiltyzitczz z.it
1.20 INNER PRODUCTLENGTH DISTANCEE
There are many waysto
multiply vectors
Last time solar multiplication
Input vector output vectorreal
THE INNER PRODUCT OR
DOT PRODUCT hes
input 2 vectors output real
IN COORDINATES
x y 2170 Xa Yz Zz
X xztyiyztz TE2 ae
E o 1,2 47013,3 2
31 6 8 1
GEOMETRICALLY
A BIT COMPLICATED
RelatingLet E Cain EIR
r Kangfatty
Fuori
So flustfot FEworks in 3D too
Ex we c
find the distance from
f Cia 47to 10,1 1 Q
Imeeee
P Q 1,44 coil 1 111,3
Hp All f ff 3.31
SOME PROPERTIES
Let DEIR try.IE R2CorlR3
AI dir w D Fair
commutes w
Scalarmulkplicatu
I olv tw t U ovtu.lv
destrinthe
C i J Foucommutative
MORE GEOMETRYof the DOT PRODUCT
If I RT
Pointone
product oftowegesizott
Theoreira For any pairof 2D fr 3D vectors
I w i
tow AFRAWAH cos
THEPOINTI cos corrects
for when I I don't point
in the same direction