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Diketahui segitiga ABC dengan , , . Proyeksi vektor  terhadap  adalah ...

Pertanyaan

Diketahui segitiga ABC dengan straight A left parenthesis 2 comma space minus 1 comma space minus 3 right parenthesis, straight B left parenthesis negative 1 comma space 1 comma space minus 11 right parenthesisstraight C left parenthesis 4 comma space minus 3 comma space minus 2 right parenthesis. Proyeksi vektor AB with rightwards arrow on top terhadap AC with rightwards arrow on top adalah ...

Pembahasan Soal:

Diketahui segitiga ABC dengan straight A left parenthesis 2 comma space minus 1 comma space minus 3 right parenthesis, straight B left parenthesis negative 1 comma space 1 comma space minus 11 right parenthesisstraight C left parenthesis 4 comma space minus 3 comma space minus 2 right parenthesis, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell AB with rightwards arrow on top end cell equals cell straight B minus straight A end cell row blank equals cell left parenthesis negative 1 comma space 1 comma space minus 11 right parenthesis minus left parenthesis 2 comma space minus 1 comma space minus 3 right parenthesis end cell row blank equals cell left parenthesis negative 1 minus 2 comma space 1 minus left parenthesis negative 1 right parenthesis comma space minus 11 minus left parenthesis negative 3 right parenthesis right parenthesis end cell row blank equals cell left parenthesis negative 3 comma space 2 comma space minus 8 right parenthesis end cell row blank blank blank row cell AC with rightwards arrow on top end cell equals cell straight C minus straight A end cell row blank equals cell left parenthesis 4 comma space minus 3 comma space minus 2 right parenthesis minus left parenthesis 2 comma space minus 1 comma space minus 3 right parenthesis end cell row blank equals cell left parenthesis 4 minus 2 comma space minus 3 minus left parenthesis negative 1 right parenthesis comma space minus 2 minus left parenthesis negative 3 right parenthesis right parenthesis end cell row blank equals cell left parenthesis 2 comma space minus 2 comma space 1 right parenthesis end cell end table

Misalkan proyeksi vektor AB with rightwards arrow on top terhadap AC with rightwards arrow on top adalah c with rightwards arrow on top, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell c with rightwards arrow on top end cell equals cell fraction numerator AB with rightwards arrow on top. AC with rightwards arrow on top over denominator open vertical bar AC with rightwards arrow on top close vertical bar squared end fraction cross times AC with rightwards arrow on top end cell row blank equals cell fraction numerator negative 3 cross times 2 plus 2 cross times left parenthesis negative 2 right parenthesis plus negative 8 cross times 1 over denominator open parentheses square root of 2 squared plus left parenthesis negative 2 right parenthesis squared plus 1 end root close parentheses squared end fraction cross times open parentheses 2 i with hat on top minus 2 j with hat on top plus k with hat on top close parentheses end cell row blank equals cell fraction numerator negative 6 plus left parenthesis negative 4 right parenthesis plus left parenthesis negative 8 right parenthesis over denominator 9 end fraction cross times open parentheses 2 i with hat on top minus 2 j with hat on top plus k with hat on top close parentheses end cell row blank equals cell negative 2 open parentheses 2 i with hat on top minus 2 j with hat on top plus k with hat on top close parentheses end cell row blank equals cell negative 4 i with hat on top plus 4 j with hat on top minus 2 k with hat on top end cell end table 

 Jadi, Proyeksi vektor AB with rightwards arrow on top terhadap AC with rightwards arrow on top adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 4 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell i with hat on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 4 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell j with hat on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell k with hat on top end cell end table 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 03 Juni 2021

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