Roboguru

1. Jika , buktikan bahwa ketiga vektor tersebut saling tegak lurus.

Pertanyaan

1. Jika a with rightwards arrow on top equals open parentheses table row 2 row 3 row 1 end table close parentheses comma space b with rightwards arrow on top equals open parentheses table row 5 row cell negative 2 end cell row cell negative 4 end cell end table close parentheses comma space dan space c with rightwards arrow on top equals open parentheses table row 10 row cell negative 13 end cell row 19 end table close parentheses, buktikan bahwa ketiga vektor tersebut saling tegak lurus.space  

Pembahasan Soal:

Vektor a with rightwards arrow on top comma space b with rightwards arrow on top comma space dan space c with rightwards arrow on top dikatakan saling tegak lurus jika

 a with rightwards arrow on top times b with rightwards arrow on top equals 0 a with rightwards arrow on top times c with rightwards arrow on top equals 0 b with rightwards arrow on top times c with rightwards arrow on top equals 0 

Perhatikan penghitungan berikut!

 a with rightwards arrow on top times b with rightwards arrow on top equals open parentheses table row 2 row 3 row 1 end table close parentheses times open parentheses table row 5 row cell negative 2 end cell row cell negative 4 end cell end table close parentheses equals 2 open parentheses 5 close parentheses plus 3 open parentheses negative 2 close parentheses plus 1 open parentheses negative 4 close parentheses equals 0 a with rightwards arrow on top times c with rightwards arrow on top equals open parentheses table row 2 row 3 row 1 end table close parentheses times open parentheses table row 10 row cell negative 13 end cell row 19 end table close parentheses equals 2 open parentheses 10 close parentheses plus 3 open parentheses negative 13 close parentheses plus 1 open parentheses 19 close parentheses equals 0 b with rightwards arrow on top times c with rightwards arrow on top equals open parentheses table row 5 row cell negative 2 end cell row cell negative 4 end cell end table close parentheses times open parentheses table row 10 row cell negative 13 end cell row 19 end table close parentheses equals 5 open parentheses 10 close parentheses plus open parentheses negative 2 close parentheses open parentheses negative 13 close parentheses plus open parentheses negative 4 close parentheses open parentheses 19 close parentheses equals 0  

Jadi, terbukti bahwa vektor a with rightwards arrow on top comma space b with rightwards arrow on top comma space dan space c with rightwards arrow on top saling tegak lurus.space 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 Juni 2021

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