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Pertanyaan

Diketahui titik P open parentheses 2 comma space 3 close parentheses dan titik Q open parentheses negative 5 comma space 4 close parentheses. Tentukan:

a. vektor stack P Q with rightwards arrow on top,

b. vektor stack Q P with rightwards arrow on top,

c. open vertical bar stack P Q with rightwards arrow on top close vertical bar

H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

vektor stack text PQ end text with rightwards arrow on top equals open parentheses table row cell negative 7 end cell row 1 end table close parenthesesstack text QP end text with rightwards arrow on top equals open parentheses table row 7 row cell negative 1 end cell end table close parentheses, dan open vertical bar stack text PQ end text with rightwards arrow on top close vertical bar equals 5 square root of 2.

Pembahasan

Jika terdapat dua buah titik text A end text open parentheses a subscript 1 comma space a subscript 1 close parentheses dan text B end text open parentheses b subscript 1 comma space b subscript 2 close parentheses, maka dapat dibuat vektor posisi di titik text A end text dan text B end text, masing-masing dinyatakan oleh vektor a with rightwards arrow on top equals open parentheses table row cell a subscript 1 end cell row cell a subscript 2 end cell end table close parentheses dan b with rightwards arrow on top equals open parentheses table row cell b subscript 1 end cell row cell b subscript 2 end cell end table close parentheses. Vektor posisi dari segmen garis berarah stack text AB end text with rightwards arrow on top dinyatakan sebagai berikut.

stack text AB end text with rightwards arrow on top equals b with rightwards arrow on top minus a with rightwards arrow on top equals open parentheses table row cell b subscript 1 minus a subscript 1 end cell row cell b subscript 2 minus a subscript 2 end cell end table close parentheses

Jika a with rightwards arrow on top equals open parentheses table row x row y end table close parentheses, maka panjang vektor a with rightwards arrow on top dapat ditentukan dengan rumus berikut.

open vertical bar a with rightwards arrow on top close vertical bar equals square root of x squared plus y squared end root

a. Vektor stack text PQ end text with rightwards arrow on top dapat dinyatakan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell stack text PQ end text with rightwards arrow on top end cell equals cell q with rightwards arrow on top minus p with rightwards arrow on top end cell row blank equals cell open parentheses table row cell negative 5 end cell row 4 end table close parentheses minus open parentheses table row 2 row 3 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 5 minus 2 end cell row cell 4 minus 3 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 7 end cell row 1 end table close parentheses end cell end table

b. Vektor stack text QP end text with rightwards arrow on top dapat dinyatakan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell stack text QP end text with rightwards arrow on top end cell equals cell p with rightwards arrow on top minus q with rightwards arrow on top end cell row blank equals cell open parentheses table row 2 row 3 end table close parentheses minus open parentheses table row cell negative 5 end cell row 4 end table close parentheses end cell row blank equals cell open parentheses table row cell 2 plus 5 end cell row cell 3 minus 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row 7 row cell negative 1 end cell end table close parentheses end cell end table

c. Panjang vektor stack text PQ end text with rightwards arrow on top adalah sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar stack text PQ end text with rightwards arrow on top close vertical bar end cell equals cell square root of x squared plus y squared end root end cell row blank equals cell square root of open parentheses negative 7 close parentheses squared plus open parentheses 1 close parentheses squared end root end cell row blank equals cell square root of 49 plus 1 end root end cell row blank equals cell square root of 50 end cell row blank equals cell 5 square root of 2 end cell end table

Dengan demikian, vektor stack text PQ end text with rightwards arrow on top equals open parentheses table row cell negative 7 end cell row 1 end table close parenthesesstack text QP end text with rightwards arrow on top equals open parentheses table row 7 row cell negative 1 end cell end table close parentheses, dan open vertical bar stack text PQ end text with rightwards arrow on top close vertical bar equals 5 square root of 2.

127

5.0 (2 rating)

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