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Diketahui  dan , tentukanlah: a. proyeksi vektor ...

Diketahui a with rightwards arrow on top equals 2 i with rightwards arrow on top minus 3 j with rightwards arrow on top plus 6 k with rightwards arrow on top dan b with rightwards arrow on top equals i with rightwards arrow on top plus 5 j with rightwards arrow on top plus 3 k with rightwards arrow on top, tentukanlah:

a. proyeksi vektor orthogonal b with rightwards arrow on top pada a with rightwards arrow on top

Jawaban:

Vektor a with rightwards arrow on top equals open parentheses 2 comma negative 3 comma 6 close parentheses dan vektor b with rightwards arrow on top equals open parentheses 1 comma 5 comma 3 close parentheses.

Proyeksi vektor orthogonal b with rightwards arrow on top pada a with rightwards arrow on top sebagai berikut:

table attributes columnalign right center left columnspacing 0px end attributes row blank equals cell open parentheses fraction numerator a with rightwards arrow on top times b with rightwards arrow on top over denominator open vertical bar a with rightwards arrow on top close vertical bar squared end fraction close parentheses times a with rightwards arrow on top end cell row blank equals cell open parentheses fraction numerator open parentheses 2 comma negative 3 comma 6 close parentheses times open parentheses 1 comma 5 comma 3 close parentheses over denominator square root of 2 squared plus open parentheses negative 3 close parentheses squared plus 6 squared end root end fraction close parentheses times open parentheses 2 comma negative 3 comma 6 close parentheses end cell row blank equals cell open parentheses fraction numerator open parentheses 2 times 1 close parentheses plus open parentheses negative 3 times 5 close parentheses plus open parentheses 6 times 3 close parentheses over denominator square root of 49 end fraction close parentheses times open parentheses 2 comma negative 3 comma 6 close parentheses end cell row blank equals cell open parentheses fraction numerator 2 minus 15 plus 18 over denominator 7 end fraction close parentheses times open parentheses 2 comma negative 3 comma 6 close parentheses end cell row blank equals cell 5 over 7 times open parentheses 2 comma negative 3 comma 6 close parentheses end cell row blank equals cell open parentheses 10 over 7 comma fraction numerator negative 15 over denominator 7 end fraction comma 30 over 7 close parentheses end cell end table  

Jadi, proyeksi vektor orthogonal b with rightwards arrow on top pada a with rightwards arrow on top adalah open parentheses 10 over 7 comma negative 15 over 7 comma 30 over 7 close parentheses.

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