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Vektor posisi titik  dan  adalah . Hitunglah: d. Besar sudut antara vektor .

Pertanyaan

Vektor posisi titik begin mathsize 14px style straight A left parenthesis negative 3 comma space minus 5 comma space 2 right parenthesis end style dan begin mathsize 14px style straight B left parenthesis 2 comma space minus 3 comma space 5 right parenthesis end style adalah begin mathsize 14px style a with rightwards arrow on top space d a n space b with rightwards arrow on top end style. Hitunglah:

d. Besar sudut antara vektor begin mathsize 14px style a with rightwards arrow on top space dan space b with rightwards arrow on top end style

Pembahasan Soal:

diketahui:

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top end cell equals cell left parenthesis negative 3 comma negative 5 comma 2 right parenthesis end cell row cell b with rightwards arrow on top end cell equals cell left parenthesis 2 comma negative 3 comma 5 right parenthesis end cell end table 

mencari perkalian titik kedua vektor tersebut:

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top times b with rightwards arrow on top end cell equals cell left parenthesis negative 3 right parenthesis left parenthesis 2 right parenthesis plus left parenthesis negative 5 right parenthesis left parenthesis negative 3 right parenthesis plus left parenthesis 2 right parenthesis left parenthesis 5 right parenthesis end cell row blank equals cell left parenthesis negative 6 right parenthesis plus 15 plus 10 end cell row blank equals 19 end table 

mencari panjang vektor:

 table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar a with rightwards arrow on top close vertical bar end cell equals cell square root of left parenthesis negative 3 right parenthesis squared plus left parenthesis negative 5 right parenthesis squared plus 2 to the power of 2 end exponent end root end cell row blank equals cell square root of 9 plus 25 plus 4 end root end cell row blank equals cell square root of 38 end cell end table 

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar b with rightwards arrow on top close vertical bar end cell equals cell square root of 2 squared plus left parenthesis negative 3 right parenthesis squared plus 5 to the power of 2 end exponent end root end cell row blank equals cell square root of 4 plus 9 plus 25 end root end cell row blank equals cell square root of 38 end cell end table  

Besar sudut antara dua vektor ditentukan dengan:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos space theta end cell equals cell fraction numerator a with rightwards arrow on top times b with rightwards arrow on top over denominator open vertical bar a with rightwards arrow on top close vertical bar open vertical bar b with rightwards arrow on top close vertical bar end fraction end cell row cell cos space theta end cell equals cell fraction numerator 19 over denominator square root of 38 times square root of 38 end fraction end cell row cell cos space theta end cell equals cell 1 half end cell row theta equals cell 60 degree end cell end table end style 

Jadi, besar sudut antara dua vektor tersebut adalah begin mathsize 14px style bottom enclose bold 60 bold degree end enclose end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 05 Mei 2021

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