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Tentukan besar vektor berikut beserta vektor satua...

Tentukan besar vektor berikut beserta vektor satuannya.

b. begin mathsize 14px style w with rightwards arrow on top equals negative i with rightwards arrow on top plus 5 j with rightwards arrow on top plus k with rightwards arrow on top end style 

Jawaban:

Besar vektor begin mathsize 14px style w with rightwards arrow on top end style adalah sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar w with rightwards arrow on top close vertical bar end cell equals cell square root of x squared plus y squared plus z squared end root end cell row blank equals cell square root of open parentheses negative 1 close parentheses squared plus 5 squared plus 1 squared end root end cell row blank equals cell square root of 27 end cell row blank equals cell 3 square root of 3 end cell end table end style

Vektor satuan dari begin mathsize 14px style w with rightwards arrow on top end style dapat ditentukan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell w with hat on top end cell equals cell fraction numerator w with rightwards arrow on top over denominator open vertical bar w with rightwards arrow on top close vertical bar end fraction end cell row blank equals cell fraction numerator 1 over denominator 3 square root of 3 end fraction open parentheses table row cell negative 1 end cell row 5 row 1 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 over 9 square root of 3 end cell row cell 5 over 9 square root of 3 end cell row cell 1 over 9 square root of 3 end cell end table close parentheses end cell end table end style

Dengan demikian vektor satuan dari begin mathsize 14px style w with rightwards arrow on top end style adalah 

begin mathsize 14px style w with hat on top equals negative 1 over 9 square root of 3 i with rightwards arrow on top plus 5 over 9 square root of 3 j with rightwards arrow on top plus 1 over 9 square root of 3 k with rightwards arrow on top end style

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