MKL 16 Vektor Dot Cross

7/25/2019 MKL 16 Vektor Dot Cross

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Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.idProgram Teknologi Informasi & Ilmu Komputer U

u. v! "u" "v" cos

uv

xy

z


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u. v! 0

vBUKAN#ektor noluBUKAN#ektor nol

|v" $ 0

|u" $ 0

u. v! "u" "v" cos

cos = 0

= 90oortogonal


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u. v! "u" "v" cos

uv

xy

z

P

%


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uv

xy

z

P

%

! "u"' "v" "u""v" cos |P%|


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uv

xy

z

P

%

! "u"' "v" "u""v" cos |v u|


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uv

xy

z

P

%

! "u"' "v" |v u|"u""v" cos


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uv

xy

z

P

%

! ()"u"' "v" |v u|*u. v


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uv

xy

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%

!xux

v'y

uy

v'z

uz

vu. v


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uv

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z

)xu+y

u+z

u*

)xv+y

v+z

v*

,u

-u

u

,v -v v


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u, v!,

u-

u

u

,v-vv+ +

,u-

u

u

,v-vv

,u-

u

u

,v-vv


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! 0-uz

vz

uy

v+

ux

vx

uz

v+ ,

uy

vy

ux

v1

u, v-u u ,u u ,u -u

, ,-

v

v,

v

v,

v-

v

!


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u! )2+ 3+ 4*

v! )3+ 5+ 4*

Tentukanu, v&v, u


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xy

z

u v

u, v


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x

y

z

u

v

v, u


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! )-u

zv

zu

yv

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xv

xu

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v'y

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uz

v*

.........

"u" "v" )u.v*

! "u""v")u.v*

6agrange identit-


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"u, v" ! "u""v")u.v*! "u""v")"u""v" cos *

! "u""v" )3 cos*

! "u""v" sin

"u, v" ! "u""v"sin

MKL 16 Vektor Dot Cross

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