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Diketahui vektor p​=(125​), vektor q​=(7​3​), dan vektor r=p​+q​. Tentukan: c. vektor satuan dari vektor p​, vektor q​, dan vektor r.

Pertanyaan

Diketahui vektor p with rightwards arrow on top equals open parentheses table row 12 row 5 end table close parentheses, vektor q with rightwards arrow on top equals open parentheses table row cell square root of 7 end cell row 3 end table close parentheses, dan vektor r with rightwards arrow on top equals p with rightwards arrow on top plus q with rightwards arrow on top. Tentukan:

c. vektor satuan dari vektor p with rightwards arrow on top, vektor q with rightwards arrow on top, dan vektor r with rightwards arrow on top.

H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

vektor satuan dari p with rightwards arrow on top adalah open parentheses table row cell 12 over 13 end cell row cell 5 over 13 end cell end table close parentheses, vektor satuan dari q with rightwards arrow on top adalah open parentheses table row cell fraction numerator square root of 7 over denominator 4 end fraction end cell row cell 3 over 4 end cell end table close parentheses, dan vektor satuan dari r with rightwards arrow on top adalah fraction numerator 1 over denominator square root of 215 plus 24 square root of 7 end root end fraction open parentheses table row cell 12 plus square root of 7 end cell row 8 end table close parentheses

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut, yaitu vektor satuan dari p with rightwards arrow on top adalah open parentheses table row cell 12 over 13 end cell row cell 5 over 13 end cell end table close parentheses, vektor satuan dari q with rightwards arrow on top adalah open parentheses table row cell fraction numerator square root of 7 over denominator 4 end fraction end cell row cell 3 over 4 end cell end table close parentheses, dan vektor satuan dari r with rightwards arrow on top adalah fraction numerator 1 over denominator square root of 215 plus 24 square root of 7 end root end fraction open parentheses table row cell 12 plus square root of 7 end cell row 8 end table close parentheses.

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:

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 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 

Misalkan diketahui vektor a with rightwards arrow on top equals open parentheses table row cell x subscript a end cell row cell y subscript a end cell end table close parentheses dan vektor b with rightwards arrow on top equals open parentheses table row cell x subscript b end cell row cell y subscript b end cell end table close parentheses. Jika c with rightwards arrow on top equals a with rightwards arrow on top plus b with rightwards arrow on top, maka vektor c with rightwards arrow on top ditentukan oleh:

c with rightwards arrow on top equals open parentheses table row cell x subscript a end cell row cell y subscript a end cell end table close parentheses plus open parentheses table row cell x subscript b end cell row cell y subscript b end cell end table close parentheses equals open parentheses table row cell x subscript a plus x subscript b end cell row cell y subscript a plus y subscript b end cell end table close parentheses

Vektor satuan dari vektor p with rightwards arrow on top equals open parentheses table row 12 row 5 end table close parentheses adalah 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 1 over denominator square root of 12 squared plus 5 squared end root end fraction open parentheses table row 12 row 5 end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator square root of 144 plus 25 end root end fraction open parentheses table row 12 row 5 end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator square root of 169 end fraction open parentheses table row 12 row 5 end table close parentheses end cell row blank equals cell 1 over 13 open parentheses table row 12 row 5 end table close parentheses end cell row blank equals cell open parentheses table row cell 12 over 13 end cell row cell 5 over 13 end cell end table close parentheses end cell end table

Vektor satuan dari vektor q with rightwards arrow on top equals open parentheses table row cell square root of 7 end cell row 3 end table close parentheses adalah 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 1 over denominator square root of open parentheses square root of 7 close parentheses squared plus 3 squared end root end fraction open parentheses table row cell square root of 7 end cell row 3 end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator square root of 7 plus 9 end root end fraction open parentheses table row cell square root of 7 end cell row 3 end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator square root of 16 end fraction open parentheses table row cell square root of 7 end cell row 3 end table close parentheses end cell row blank equals cell 1 fourth open parentheses table row cell square root of 7 end cell row 3 end table close parentheses end cell row blank equals cell open parentheses table row cell fraction numerator square root of 7 over denominator 4 end fraction end cell row cell 3 over 4 end cell end table close parentheses end cell end table

Vektor r with rightwards arrow on top adalah sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell r with rightwards arrow on top end cell equals cell p with rightwards arrow on top plus q with rightwards arrow on top end cell row blank equals cell open parentheses table row 12 row 5 end table close parentheses plus open parentheses table row cell square root of 7 end cell row 3 end table close parentheses end cell row blank equals cell open parentheses table row cell 12 plus square root of 7 end cell row 8 end table close parentheses end cell end table

Vektor satuan dari vektor r with rightwards arrow on top, yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell e with hat on top end cell equals cell fraction numerator 1 over denominator square root of open parentheses 12 plus square root of 7 close parentheses squared plus 8 squared end root end fraction open parentheses table row cell 12 plus square root of 7 end cell row 8 end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator square root of 215 plus 24 square root of 7 end root end fraction open parentheses table row cell 12 plus square root of 7 end cell row 8 end table close parentheses end cell end table

Dengan demikian, vektor satuan dari p with rightwards arrow on top adalah open parentheses table row cell 12 over 13 end cell row cell 5 over 13 end cell end table close parentheses, vektor satuan dari q with rightwards arrow on top adalah open parentheses table row cell fraction numerator square root of 7 over denominator 4 end fraction end cell row cell 3 over 4 end cell end table close parentheses, dan vektor satuan dari r with rightwards arrow on top adalah fraction numerator 1 over denominator square root of 215 plus 24 square root of 7 end root end fraction open parentheses table row cell 12 plus square root of 7 end cell row 8 end table close parentheses

67

4.8 (5 rating)

Pertanyaan serupa

Diketahui vektor p​=(125​), vektor q​=(7​3​), dan vektor r=p​+q​. Tentukan: b. panjang dari vektor p​, vektor q​, dan vektor r.

38

4.1

Jawaban terverifikasi

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