Pertanyaan

Jika vector u = ( 3 , − 4 ) dan v = ( 5 , 2 ) , maka proyeksi scalar orthogonal vector ( u − v ) pada vector u + v adalah ...

Jika vector $u = (3, - 4)$ dan $v = (5, 2)$ , maka proyeksi scalar orthogonal vector $(u - v)$ pada vector $u + v$ adalah ...

G. Albiah

Master Teacher

Mahasiswa/Alumni Universitas Galuh Ciamis

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Pembahasan

Proyeksi skalar ortogonal suatu vektor pada vektor lain adalah : Proyeksi vektor orthogonal pada Proyeksi vektor orthogonal pada Diketahui vector dan , cari duluvector danvector , Maka di dapatkan dan . Proyeksi scalar orthogonal vector pada vector , Jadi,proyeksi scalar orthogonal vector pada vector adalah .

Proyeksi skalar ortogonal suatu vektor pada vektor lain adalah :

Proyeksi vektor orthogonal pada $u with rightwards arrow on top space equals fraction numerator u with rightwards arrow on top times v with rightwards arrow on top over denominator open vertical bar u with rightwards harpoon with barb upwards on top close vertical bar end fraction$
Proyeksi vektor orthogonal pada $v with rightwards arrow on top space equals fraction numerator v with rightwards arrow on top times u with rightwards arrow on top over denominator open vertical bar v with rightwards arrow on top close vertical bar end fraction$

Diketahui vector u equals left parenthesis 3 comma negative 4 right parenthesis dan v equals left parenthesis 5 comma 2 right parenthesis , cari dulu vector left parenthesis u minus v right parenthesis dan vector u plus v ,

Maka di dapatkan u plus v equals left parenthesis 8 comma negative 2 right parenthesis dan u minus v equals left parenthesis negative 2 comma negative 6 right parenthesis .

Proyeksi scalar orthogonal vector left parenthesis u minus v right parenthesis pada vector u plus v ,

$table attributes columnalign right center left columnspacing 0px end attributes row blank equals cell fraction numerator open parentheses u plus v close parentheses open parentheses u minus v close parentheses over denominator open vertical bar u minus v close vertical bar end fraction end cell row blank equals cell fraction numerator open square brackets table row 8 row cell negative 2 end cell end table close square brackets times open square brackets table row cell negative 2 end cell row cell negative 6 end cell end table close square brackets over denominator square root of left parenthesis negative 2 right parenthesis squared plus left parenthesis negative 6 right parenthesis squared end root end fraction end cell row blank equals cell fraction numerator open square brackets table row cell 8 times negative 2 end cell row cell negative 2 times negative 6 end cell end table close square brackets over denominator square root of 40 end fraction end cell row blank equals cell fraction numerator open square brackets table row cell negative 16 end cell row 12 end table close square brackets over denominator square root of 40 end fraction end cell row blank equals cell fraction numerator open square brackets table row cell negative 16 end cell row 12 end table close square brackets over denominator square root of 4 cross times 10 end root end fraction end cell row blank equals cell fraction numerator open square brackets table row cell negative 16 end cell row 12 end table close square brackets over denominator 2 square root of 10 end fraction end cell row blank equals cell open square brackets table row cell fraction numerator negative 16 over denominator 2 square root of 10 end fraction end cell row cell fraction numerator 12 over denominator 2 square root of 10 end fraction end cell end table close square brackets space rasionalkan end cell row blank equals cell open square brackets table row cell fraction numerator negative 16 over denominator 2 square root of 10 end fraction cross times fraction numerator square root of 10 over denominator square root of 10 end fraction end cell row cell fraction numerator 12 over denominator 2 square root of 10 end fraction cross times fraction numerator square root of 10 over denominator square root of 10 end fraction end cell end table close square brackets end cell row blank equals cell open square brackets table row cell fraction numerator negative 16 square root of 10 over denominator 2 times 10 end fraction end cell row cell fraction numerator 12 square root of 10 over denominator 2 times 10 end fraction end cell end table close square brackets end cell row blank equals cell open square brackets table row cell fraction numerator negative 16 square root of 10 over denominator 20 end fraction end cell row cell fraction numerator 12 square root of 10 over denominator 20 end fraction end cell end table close square brackets space sederhanakan end cell row blank equals cell open square brackets table row cell negative 4 over 5 square root of 10 end cell row cell 3 over 5 square root of 10 end cell end table close square brackets end cell end table$

Jadi, proyeksi scalar orthogonal vector left parenthesis u minus v right parenthesis pada vector u plus v adalah open parentheses negative 4 over 5 square root of 10 comma space 3 over 5 square root of 10 close parentheses .

Latihan Bab

Pengertian dan Operasi Vektor I

Operasi Vektor II

Kedudukan Vektor

Aljabar Vektor I

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