Diketahui panjang vektor , panjang vektor dan besar sudut antara vektor dan adalah . Tentukan panjang vektor

Diketahui panjang vektor $begin mathsize 14px style straight a with rightwards arrow on top equals negative 6 end style$ , panjang vektor $begin mathsize 14px style straight b with rightwards arrow on top equals 4 end style$ dan besar sudut antara vektor $begin mathsize 14px style straight a with rightwards arrow on top end style$ dan $begin mathsize 14px style straight b with rightwards arrow on top end style$ adalah $begin mathsize 14px style 90 degree end style$ . Tentukan panjang vektor $begin mathsize 14px style open vertical bar straight a with rightwards arrow on top minus straight b with rightwards arrow on top close vertical bar end style$

Jawaban:

diketahui :

$begin mathsize 14px style open vertical bar straight a with rightwards arrow on top close vertical bar equals negative 6 open vertical bar straight b with rightwards arrow on top close vertical bar equals 4 space space space straight theta equals 90 degree end style$

Ditanya : $begin mathsize 14px style open vertical bar straight a with rightwards arrow on top minus straight b with rightwards arrow on top close vertical bar end style$ = ...?

Jawab :

$begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell open vertical bar straight a with rightwards harpoon with barb upwards on top minus straight b with rightwards harpoon with barb upwards on top close vertical bar end cell equals cell square root of straight a squared plus straight b squared minus straight a times straight b times cos space 90 degree end root end cell row blank equals cell square root of open parentheses negative 6 close parentheses squared plus open parentheses 4 close parentheses squared minus open parentheses negative 6 close parentheses times open parentheses 4 close parentheses times 0 end root end cell row blank equals cell square root of 36 plus 16 end root end cell row blank equals cell square root of 52 end cell row blank equals cell 2 square root of 13 end cell end table end style$

Jadi, $begin mathsize 14px style open vertical bar straight a with rightwards arrow on top minus straight b with rightwards arrow on top close vertical bar end style$ = $begin mathsize 14px style 2 square root of 13 end style$

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