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Diketahui vektor p​=(6−4​). Tentukan vektor satuan dari vektor p​.

Pertanyaan

Diketahui vektor p with bar on top equals open parentheses table row 6 row cell negative 4 end cell end table close parentheses. Tentukan vektor satuan dari vektor p with bar on top.

H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

vektor satuan dari vektor p with rightwards arrow on top adalah table attributes columnalign right center left columnspacing 0px end attributes row cell e with hat on top end cell equals cell open parentheses table row cell 3 over 13 square root of 13 end cell row cell negative 2 over 13 square root of 13 end cell end table close parentheses end cell end table.

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah table attributes columnalign right center left columnspacing 0px end attributes row cell e with hat on top end cell equals cell open parentheses table row cell 3 over 13 square root of 13 end cell row cell negative 2 over 13 square root of 13 end cell end table close parentheses end cell end table.

Misalkan vektor a with rightwards arrow on top equals open parentheses table row x row y end table close parentheses. Vektor satuan dari a with rightwards arrow on top ditentukan dengan rumus berikut.

e with hat on top equals fraction numerator a with rightwards arrow on top over denominator open vertical bar a with rightwards arrow on top close vertical bar end fraction equals fraction numerator a with rightwards arrow on top over denominator square root of x squared plus y squared end root end fraction equals fraction numerator 1 over denominator square root of x squared plus y squared end root end fraction open parentheses table row x row y end table close parentheses

Diketahui vektor p with rightwards arrow on top equals open parentheses table row 6 row cell negative 4 end cell end table close parentheses. Vektor satuan dari vektor p with rightwards arrow on top dapat ditentukan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell e with hat on top end cell equals cell fraction numerator p with rightwards arrow on top over denominator open vertical bar p with rightwards arrow on top close vertical bar end fraction end cell row blank equals cell fraction numerator 1 over denominator square root of 6 squared plus open parentheses negative 4 close parentheses squared end root end fraction open parentheses table row 6 row cell negative 4 end cell end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator square root of 36 plus 16 end root end fraction open parentheses table row 6 row cell negative 4 end cell end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator square root of 52 end fraction open parentheses table row 6 row cell negative 4 end cell end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator 2 square root of 13 end fraction open parentheses table row 6 row cell negative 4 end cell end table close parentheses end cell row blank equals cell fraction numerator square root of 13 over denominator 26 end fraction open parentheses table row 6 row cell negative 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 3 over 13 square root of 13 end cell row cell negative 2 over 13 square root of 13 end cell end table close parentheses end cell end table

Dengan demikian, vektor satuan dari vektor p with rightwards arrow on top adalah table attributes columnalign right center left columnspacing 0px end attributes row cell e with hat on top end cell equals cell open parentheses table row cell 3 over 13 square root of 13 end cell row cell negative 2 over 13 square root of 13 end cell end table close parentheses end cell end table.

301

3.3 (3 rating)

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