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Pertanyaan

Diketahui segitiga ABC dengan A(5,1,5), B(1,4,5) dan C(3,2,1). Tentukan:

b. Proyeksi vektor AC pada AB

S. Difhayanti

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. Dr. Hamka

Jawaban terverifikasi

Jawaban

proyeksi vektor AC pada AB adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses negative 44 over 25 comma 33 over 25 comma 0 close parentheses end cell end table.

Pembahasan

Ingat kembali rumus proyeksi vektor berikut!

straight p equals fraction numerator stack A C with rightwards arrow on top cross times stack A B with rightwards arrow on top over denominator open vertical bar A B close vertical bar squared end fraction cross times A B

Dengan menggunakan rumus proyeksi vektor di atas, maka didapat perhitungannya sebagai berikut ini.

table attributes columnalign right center left columnspacing 0px end attributes row cell stack A C with rightwards arrow on top end cell equals cell open vertical bar stack A C with rightwards arrow on top close vertical bar end cell row blank equals cell square root of open parentheses 3 minus 5 close parentheses squared plus open parentheses 2 minus 1 close parentheses squared plus open parentheses 1 minus 5 close parentheses squared end root end cell row blank equals cell square root of 4 plus 1 plus 16 end root end cell row blank equals cell square root of 21 end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row cell stack A B with rightwards arrow on top end cell equals cell open vertical bar stack A B with rightwards arrow on top close vertical bar end cell row blank equals cell square root of open parentheses 1 minus 5 close parentheses squared plus open parentheses 4 minus 1 close parentheses squared plus open parentheses 5 minus 5 close parentheses squared end root end cell row blank equals cell square root of 16 plus 9 end root end cell row blank equals cell square root of 25 end cell row blank equals 5 end table

Proyeksi vektor AC pada AB yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row straight p equals cell fraction numerator stack A C with rightwards arrow on top cross times stack A B with rightwards arrow on top over denominator open vertical bar A B close vertical bar squared end fraction cross times A B end cell row blank equals cell fraction numerator open parentheses negative 2 close parentheses cross times open parentheses negative 4 close parentheses plus 1 cross times 3 plus open parentheses negative 4 close parentheses cross times 0 over denominator 5 squared end fraction cross times open parentheses negative 4 comma 0 comma 3 close parentheses end cell row blank equals cell 11 over 25 cross times open parentheses negative 4 comma 3 comma 0 close parentheses end cell row blank equals cell open parentheses negative 44 over 25 comma 33 over 25 comma 0 close parentheses end cell end table

Jadi, proyeksi vektor AC pada AB adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses negative 44 over 25 comma 33 over 25 comma 0 close parentheses end cell end table.

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