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Pertanyaan

Diketahui vektor-vektor: a = ( 6 0 ​ ) , b = ( − 3 − 4 ​ ) , c = ( 5 2 ​ ) , dan d = ( 4 − 1 ​ ) Tentukan vektor satuan dari a + b − 3 c !

Diketahui vektor-vektor:

Tentukan vektor satuan dari  !

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Z. Apriani

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

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Pembahasan

Ingat bahwa vektor satuan adalah vektor yang panjangnya sama dengan satu. Berdasarkan soal diketahui , sehingga panjang vektor : Jadi,vektor satuan :

Ingat bahwa vektor satuan adalah vektor yang panjangnya sama dengan satu. Berdasarkan soal diketahui straight a with rightwards arrow on top equals open parentheses table row 6 row 0 end table close parentheses comma space straight b with rightwards arrow on top equals open parentheses table row cell negative 3 end cell row cell negative 4 end cell end table close parentheses comma space straight c with rightwards arrow on top equals open parentheses table row 5 row 2 end table close parentheses comma space dan space straight d with rightwards arrow on top equals open parentheses table row 4 row cell negative 1 end cell end table close parentheses, sehingga panjang vektor straight a with rightwards arrow on top plus straight b with rightwards arrow on top minus 3 straight c with rightwards arrow on top:

table attributes columnalign right center left columnspacing 0px end attributes row cell straight a with rightwards arrow on top plus straight b with rightwards arrow on top minus 3 straight c with rightwards arrow on top end cell equals cell open parentheses table row 6 row 0 end table close parentheses plus open parentheses table row cell negative 3 end cell row cell negative 4 end cell end table close parentheses minus 3 open parentheses table row 5 row 2 end table close parentheses end cell row blank equals cell open parentheses table row 6 row 0 end table close parentheses plus open parentheses table row cell negative 3 end cell row cell negative 4 end cell end table close parentheses minus open parentheses table row 15 row 6 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 12 end cell row cell negative 10 end cell end table close parentheses end cell row cell open vertical bar straight a plus straight b minus 3 straight c close vertical bar end cell equals cell square root of left parenthesis negative 12 right parenthesis squared plus left parenthesis negative 10 right parenthesis to the power of 2 end exponent end root end cell row blank equals cell square root of 144 plus 100 end root end cell row blank equals cell square root of 244 end cell row blank equals cell 2 square root of 61 end cell end table


Jadi, vektor satuan straight a with rightwards arrow on top plus straight b with rightwards arrow on top minus 3 straight c with rightwards arrow on top:

table attributes columnalign right center left columnspacing 0px end attributes row cell vektor space satuan space straight a with rightwards arrow on top plus straight b with rightwards arrow on top minus 3 straight c with rightwards arrow on top end cell equals cell fraction numerator 1 over denominator open vertical bar straight a plus straight b minus 3 straight c close vertical bar end fraction times left parenthesis straight a with rightwards arrow on top plus straight b with rightwards arrow on top minus 3 straight c with rightwards arrow on top right parenthesis end cell row blank equals cell fraction numerator 1 over denominator 2 square root of 61 end fraction open parentheses table row cell negative 12 end cell row cell negative 10 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell fraction numerator negative 6 over denominator square root of 61 end fraction end cell row cell fraction numerator negative 5 over denominator square root of 61 end fraction end cell end table close parentheses end cell end table

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